Ok, you want to travel the distance of 56,000 light years in a few days.
As you put the "reality check" tag on your question, I am going to say this now: this is not possible.
If you traveled at the speed of light itself (which AFAIK is impossible for anything with mass) it would take you 56,000 years to reach your destination (or 20,440,000 days). And you are proposing to travel there in a few days (lets say 5 days for arguments sake).
So you are proposing to travel at over 4 million times the speed of light.
Even if you had the most accurate maps of the galaxy ever produced, traveling at that speed would destroy you, your ship, the planet Earth and anything in the nearby vicinity. Possibly even the galaxy itself.
However if you wanted to utilize some form of "Faster Than Light" (FTL) travel, then navigation becomes a different beast altogether. All methods of FTL travel are theoretical at best, but most of them involve jumping across space.
In this case navigating your way to a point 56,000 light years away is relatively easy. You find a point (or series of points) that is empty and then jump/warp/appear there.
All depends on the method of FTL travel you are employing.
You said that
Humans got a one time ticket to the other side of the galaxy, which makes me think that this is something that affects the entire human race, and not one individual.
Who produced this ticket? And assuming the ticket is a metaphor, how did we encounter this opportunity to travel to the other side of the galaxy?
I can think of two possibilities. The first is that a more advanced race is giving us this opportunity and the second is a freak phenomena, similar to a wormhole or stargate appears within a reachable distance.
In either case the position of stars on the other side of the galaxy and whether we need to navigate around them is irrelevant.
In the first possibility it will be the advanced race that does the navigating for us, and undoubtedly they will have accurate maps of the other side of the galaxy. So we don't need the maps.
In the second possibility, we will get spat out randomly on the other side of the galaxy. Due to the interference caused by the super massive black hole in the center of the galaxy we have no way of finding out the position of stars on the other side. So the wormhole could put us within the close vicinity of a star, but more likely it will put us somewhere safe.
I think you need to provide us with more information on how you are getting to the other side of the galaxy in such a short time. This will then determine how navigation can be made and whether we can make maps of the other side of the galaxy.