This is a long answer, in eight parts, with several suggestions for why travelling to other galaxies might be impractical in a space opera setting with FTL star travel. It is possible that combining two or more suggestions might work for your story.
How far do people travel in interstellar space within our galaxy in your story? That will be a big factor in determining how hard it may be to reach other galaxies.
Part One: Some Basic Astronomical Facts for Science Fiction Writers.
If there is a faster than light (FTL) drive in your story that works more or less by having the spaceship travel through all the space between star A and Star B, that travel has to be at one or more specific FTL speeds.
So it is possible there is only one single speed for FTL travel, in which case it can be set at any value an author wants for their story. Or if there are a range of possible FTL speeds, going faster may require exponentially more energy, until it would be impossible to provide enough energy to travel any faster than a specific speed.
So here is some basic useful information about the "geography" of interstellar and intergalactic space.
I note that in this region of our galaxy the typical distance between one star and the next closest star would be about four light years or five light years. And various individual stars differ in how close they are to their nearest neighbors at the moment. But as a general rule a voyage from one star to the star which is nearest to it is usually not much more or less than about four or five light years. Voyages to stars which are not the closest to one's home star can be a few times as long as that, or hundreds, or thousands of times as long as that.
Most of the stars in our galaxy are in the central bulge, which is a few thousand light years in diameter, and in the galactic disc which is about 100,000 light years in diameter and about 1,000 light years thick. So basically if your home star is on the edge of the galactic disc the farthest stars in the galactic disc will be about 100,000 thousand light years away, which is about 20,000 to 25,000 times as far as the typical distance between a star and its closest neighbor.
So as a general rule, the possible lengths of interstellar voyages within the galactic disc vary by a factor of 20,000 to 25,000. So a story where a trip from Star A to Star B takes 1 day while a trip from Star A to star C takes 10,000 years or 3,352,500 days, at the same FTL speed and within our Milky Way Galaxy, would be impossible.
The Milky Way Galaxy also has a halo of scattered globular star clusters and scattered individual stars which has a diameter of about 200,000 light years.
There are about 113 galaxies in what is called the Local group of galaxies. Most of them are tiny dwarf galaxies whose diameters are only a few thousand light years.
The distances between Earth and those 113 mostly tiny galaxies in the local group vary between 70,000 light years and 4,440,000 light years. And if the Canis Major Dwarf Galaxy actually is a galaxy (which is disputed) it is only 25,000 light years from Earth. And beyond the local group of galaxies there are billions of detectable galaxies at distances up to 13,260,000,000 light years for galaxy MACS0647-JD.
https://en.wikipedia.org/wiki/List_of_nearest_galaxies[1]
https://en.wikipedia.org/wiki/MACS0647-JD[2]
Earth is about 25,000 light years from the center of the Milky Way Galaxy, and thus about 75,000 light years from stars on the far edge of the galactic disc. Thus if FTL spaceships always travel at 75,000 light years per year, it would take about one year to travel from Earth to the far edge of the galactic disc, and also about one year to travel from Earth to the very, very nearest galaxies.
There are eight or nine tiny galaxies within a distance of 100,000 light years from Earth. So if FTL spaceshps travel at 75,000 times the speed of light, there would be eight or nine galaxies which could be reached in less than 1.333 years travel. There are 16 or 17 galaxies which could be reached in less than 2 years travel, and 22 or 23 galaxies which could be reached in less than 3 years travel, and 31 or 32 galaxies which could be reached in less than four years travel, and so on.
So if it is possible to reach every part of the Milky Way Galaxy in a voyage time which is considered acceptable and practical by future space travelers, it should be possible to reach at least a few of the nearest galaxies in an acceptable and practical voyage time.
In the region near Earth, the stellar density is about 0.004 stars per cubic light year, or about 0.14 stars per cubic parsec.
Part Two: If FTL Ships Travel at One Constant Speed.
With the stellar density in the region near Earth, a spherical volume of space with a radius of 50 light years and a diameter of 100 light years would contain about 2,096 star systems. A sphere with a diameter of 100 lightyears would spread across one thousandeth of the diameter of the Milky Way Galaxy and would look very small and unimportant in a map of the galaxy. The longest possible voyage within such a sphere would be 100 light years, about 20 to 25 times as far as a voyage from one star to its nearest neighbor star.
If between one star out of every thousand to one star out of every ten has a planet with native life, or a planet habitable for humans which they can settle, or a planet ruled by the space government in the story, or a planet with native intelligent life, or is otherwise interesting for your story, there will be about 2 to 200 such planets within that volume of space.
If a voyage of 100 light years takes 1 year, a voyage to the closest star should take about 14.6 to 18.2 days, and a voyage to a tiny exteror galaxy only 70,000 light years away should take 700 years.
There would be about 2,096,000 stars in a spherical volume of space with a radius of 500 light years and a diameter of 1,000 light years, a mere one percent of the diameter of the galactic disc. The longest voyage possible in such a sphere would be one 1,000 light years long which would be about 200 to 250 times the length of most voayages from one star to its nearest neighbor star.
If between one star out of every thousand to one star out of every ten has a planet with native life, or a planet habitable for humans which they can settle, or a planet ruled by the space government in the story, or a planet with native intelligent life, or is otherwise interesting for your story, there will be about 2,000 to 200,000 such planets within that volume of space.
If it takes one year to travel 1,000 light years, it will take about 1.4 to 1.8 days to travel from one star to its nearest neighbor, and about 70 years to travel to the nearest tiny exterior galaxy.
A cylinder shaped volume of space with a height of 1,000 light years and a radius of 500 light years would contain about 3,140,000 stars. That space would have a diameter of 1,000 light years, one percent of the diameter of the galactic disc. The longest possible voyage within that space would be 1,414 light years, about 282.8 to 353.5 times as a typical voyage from one star to its closest neightbor star.
If between one star out of every thousand to one star out of every ten has a planet with native life, or a planet habitable for humans which they can settle, or a planet ruled by the space government in the story, or a planet with native intelligent life, or is otherwise interesting for your story, there will be about 2,996 to 299,600 such planets within that volume of space.
If it takes 1 year to travel 1,414 light years, it will take about 1.03 to 1.2 days to travel from one star to its nearest neighbor, and about 49.5 years to travel to the nearest tiny exterior galaxy.
A cylinder shaped volume of space with a height of 1,000 light years and a radius of 1,000 light years would contain about 12,560,000 stars. It would be 2,000 light years in diameter, 2 percent of the diameter of the galactic disc, and the longest possible voyage within that space would be 2,236 light years long, and woud be about 447 to 559 times as long as a voyage to a star's closest neighbor star.
If between one star out of every thousand to one star out of every ten has a planet with native life, or a planet habitable for humans which they can settle, or a planet ruled by the space government in the story, or a planet with native intelligent life, or is otherwise interesting for your story, there will be about 11,984 to 1,198,400 such planets within that volume of space.
If it takes 1 year to travel 2,236 light years, it will take about 0.65 to 0.81 days to travel from one star to its nearest neighbor, and about 31.3 years to travel to the nearest tiny exterior galaxy.
So it seems to me it is perfectly acceptable from a story point of view to set the story in a vast volume of space, which is still tiny compared to the entire galaxy, and have the FTL space ships travel fast enough for the purpose of the story, and yet slow enough that voyages to even the Draco II galaxy, only 70,000 light years from Earth, would take far too long for anyone to want to make the trip, or for any ship to carry enough fuel for the voyage.
Part Three: What if FTL Ships Accelerate and Decelerate?
The above calculations were made assuming that FTL ships travel only at one single speed.
But what if FTL ships in the story accelerate at a constant rate until they are halfway to the destination and then decelerate for the rest of the voyage? In that case they would reach the average speed on the voyage at one quarter of the voyage.
If it would take 100 years at the rate of acceleration and deceleration to travel 163,000 light years to the Large Magellanic Cloud, the average speed on the voyage would be 1,630 times the speed of light, and the ship would reach that speed after 25 years of acceleration. Thus the rate of acceleration would be 65.2 light years per year per year of accelration, or 0.1785 light years per year per day of acceleration.
If nobody ever makes a voyage longer than one Earth year, they would reach the average speed in such a longest voyage after one quarter Earth year, and that average speed would be 16.3 light years per year. Thus the longest voyages people would make would be to a distance of 16.3 light years, and explored space would be a sphere about 32.6 lightyears in diameter, with a volume of 18,140.59 cubic light years and containing about 72 stars.
If a trip to the Andromeda Galaxy, 2,536,000 light years away, took 100 years at constant acceleration and deceleration, the average speed would be 25,360 times the speed of light, and would be reached after 25 years of acceleration. Thus the FTL ship would accelerate at the rate of 1,014.4 times the speed of light per year, or 2.772 times the speed of light per day.
If nobody ever makes a voyage longer than one Earth year, they would reach the average speed in such a longest voyage after one quarter Earth year, and that average speed would be 253.6 light years per year. Thus the longest voyages people would make would be to a distance of 253.6 light years, and explored space would be a sphere about 507.2 light years in diameter. Such a sphere would have a volume of about 68,300,000 cubic light years and contain about 273,200 stars.
At that acceleration it would take 44 days to travel 4 light years and 50 days to travel 5 light years.
If a trip to the Andromeda Galaxy, 2,536,000 light years away, took 50 years at constant acceleration and deceleration, the average speed would be 50,720 times the speed of light, and would be reached after 12.5 years of acceleration. Thus the FTL ship would accelerate at the rate of 4,057.6 times the speed of light per year, or 11.109 times the speed of light per day.
If nobody ever makes a voyage longer than one Earth year, they would reach the average speed in such a longest voyage after one quarter Earth year, and that average speed would be 1,014.4 light years per year. Thus the longest voyages people would make would be to a distance of 1,014.4 light years, and explored space would be a sphere about 2,028.8 light years in diameter. Such a sphere would have a volume of about 4,370,000,000 cubic light years and contain about 17,480,000 stars.
At that acceleration it would take 22 days to travel 4 light years and 25 days to travel 5 light years.
If a trip to the Andromeda Galaxy, 2,536,000 light years away, took 10 years at constant acceleration and deceleration, the average speed would be 253,600 times the speed of light, and would be reached after 2.5 years of acceleration. Thus the FTL ship would accelerate at the rate of 101,440 times the speed of light per year, or 277.275 times the speed of light per day, or 11.553 light years per hour, so the shortest interstellar voyages should take less than one hour.
If nobody ever makes a voyage longer than one Earth year, they would reach the average speed in such a longest voyage after one quarter Earth year, and that average speed would be 25,360 light years per year. Thus the longest voyages people would make would be to a distance of 25,360 light years, and explored space would be a sphere about 50,720 light years in diameter. Such a sphere should contain billions of stars.
So if FTL ships constantly accelerate and decelerate during their voyages, the math is a little more complicated, but it is still possible for FTL ships to reach a large neough number of stars withint a reasonable time while other galaxies would still take too long to reach.
Part Four: FTL is faster over short distances, slower over long distances.
This is sort of the opposite of acceleration making the ship go faster over long distances.
In the Star Trek site Trek BBS it has been commented that short voyages in Star Trek seem involve much faster speeds than long voyages do. And there are various possible reasons for that, including Sci-Fi Writers Have No Sense of Distance:
https://tvtropes.org/pmwiki/pmwiki.php/SciFiWritersHave/NoSenseOfDistance[3]
One possible theory to explain that in universe would be that a ship travelling faster than light might have to stop periodically to rest, recharge, and regenerate the FTL engines. And how often the ship has to stop, and/or how long it takes to get the engines ready to use again, might depend on how fast it was travelling. Possibly a linear increase in speed might require might be a geometric increase in down time when the engines cannot be used. If so, eventually the travel time using the faster FTL speed might equal and then surpass the travel time using a slower FTL speed, and so it would only be practical to use the fastest FTL speeds teh ship is capable of to travel short distances in emergencies. Thus the FTL ships would have an upper speed limit for long distance voyages, one which might make voyages to other galaxies have too long travel times to be practical.
And if spaceships make instantaneous jumps through space, the engines might need time to rest, recharge, and regenerate between jumps. And if the times beeween rest periods decreses geometrically with the length of the jumps through space, and/or the length of the rest periods increase geometrically with the length of the jumps, eventually making longer jumps will be just as slow as making shorter jumps, and then slower.
Possibly a jump long enough to reach another galaxy in one jump might require the engines to rest, recharge, and regenrate for decades or centuries, and the crew would all be dead before they could return to their home galaxy. And possibly the fastest total speed making many jumps and including rest periods to another galaxy would also take decades or centuries and the crew would all die before they got to the galaxy.
Part Five: Making Jumps Through Hyperspace
Maybe your ships travelby making instantaneous jumps through hyperspace. Maybe it always takes a day for a ship's engines to recharge and make another jump. Maybe the longer distance covered by a jump, the more energy it takes to jump, and the most efficient use of jump energy is to make jumps as close to ten light years long as will get you to your destination.
Suppose that even a one man ship, with supplies to keep only one person alive, and with the rest of the ship crammed with the jump engines and the energy suppy for the jumps, can only carry enough energy and supplies for a thousand jumps, and thus a round trip of 10,000 light years, which would have to be 5,000 light years out and 5,000 light years back to civilization so the pilot avoids dying in space.
At a maximum speed of 10 light years per day, If nobody was willing to make a voyage longer than one year long, the explored volume of the galaxy would be a sphere with a radius of 3,652.5 light years and a diameter of 7,305 light years. That sphere would have a volumeof about 204,000,000,000 cubic light years, and it the density of stars was the same as in our region of the galaxy, it would contain about 816,000,000 stars, less than one percent of the stars in the Milky Way Galaxy. However, such a sphere of space would be large enough that there would probably be considerable variation in stellar density within it.
With ships able to make one jump of several light years per day, it should take less than one day to make the shortest interstellar voyages.
Part Six: A Galactic Barrier
In the second Star Trek pilot episode "Where No Man Has Gone Before" the Enterprise encountered an energy barrier around the Milky Way Galaxy which caused significant damage to it.
In "By Any Other Name" a ship from the Andromeda Galaxy was damaged crossing the energy barrier and its crew abandoned it and used lifeboats to reach a planet.
So possibly in your story there might be an energy barrier at the edge of the Milky Way Galaxy. And possibly any ship which tries to cross it is destroyed.
And that energy barrier might be an artificial force shield designed to protect the Milky Way Galaxy from Something Outside. And possibly your heroes discover that the Something Outside is trying to break through the barrier.
Or maybe the artificial force shield was designed to protect the rest of the universe from the horrors within our galaxy. And possibly in your story the surviors of the human race are in a "rag tag fugitive fleet" seeking to leave the Milky Way Galaxy and flee to another galaxy for survival, but the force shield keeps their ships from leaving the Milky Way as the menace gets closer and closer.
Par Seven: No Travel Between Galaxies in Asimov's Foundation Series
This question asked why humans didn't try to settle other galaxies in Asimov's Foundation series.
https://scifi.stackexchange.com/questions/60083/why-didnt-humans-try-to-settle-other-galaxies[4]
And possibly some of the comments and answers there may suggest something to you.
Part Eight: Maybe FTL drive is faster in denser space.
It seems logical to me that a FTL drive might be faster in interstellar space than in interplanetary space, and faster in intergalactic space than in interstellar space.
And the same thing seemed logical to E.E. Smith in his Lensman series. In Gray Lensman, when Kimball Kinneson sets out in the Dauntless to investigate the Second galaxy, home of the forces of Boskone, they discover that the cosmic energy (not to be confused with cosmic rays) they can capture to power their space drive is much more abundant in intergalactic space, while the particle density to slow down the ship with friction is much less. The two factors combined enabled the Dauntless to travel much faster in intergalactic space than inside our galaxy.
But possibly in some science fiction stories the reverse might be true.
Possibly the space drive paradoxically works better where the density of ions, atoms, molecules, and dust particles in space is higher, instead of being slowed by having to deal with them.
Or maybe the FTL space drive works better in more warped space. The more that space is warped by gravity, the faster the ship can travel. And the degree to which space is warped by gravity depends on how close and how massive various astronomical bodies are.
So within our galaxy, the FTL ship would go faster the closer it was to the central bulge of the galaxy, and slower the farther it was from the central bulge.
And outside our galaxy, the ship would go slower the farther it got from our galaxy until it got close enough to the target galaxy for that galaxy's gravity to be stronger than our galaxy's gravity.
And if the space drive involves making instant jumps from one point to another, maybe they can be longer jumps in more warped space and shorter jumps in less warped space.