Depending on the density of fuel you are looking for, exactly what fuel you need, and how protected you are from heat and radiation, I would say your best bets for refueling a fusion-powered spacecraft are interstellar gas, gas giant planets, ocean/ice planets, and red giant stars.
The easiest reaction for nuclear fusion (requiring the least temperature and pressure to fuse) is deuterium plus tritium. Both of these are isotopes of hydrogen, with one and two neutrons, respectively. Normal hydrogen, also known as "protium", has no neutrons, only a proton and an electron. Tritium is radioactive with a half-life of 12 years, so there are no long-lived stocks of it to collect. We will skip this possibility for now.
The next best reaction is deuterium + deuterium. Deuterium is stable, and was produced in the big bang along with protium and helium, and so it is a (very small) fraction of the interstellar gas, which is also what forms stars and gas giant planets; the primordial fraction is about 27 parts per million of the total hydrogen. This is similar to the fraction found in gas clouds, newborn stars, and gas giant planets, and you are unlikely to find it in higher concentrations on a truly large scale anywhere in the universe, although it can be expected to be somewhat enriched on terrestrial planets, because it is slightly more resistant to being blown away by stellar wind than normal hydrogen. For instance, on earth it is 156 ppm of hydrogen.
Moving down the list, the next fuel you might be interested in is ³He, the rarer isotope of helium. Its cosmological abundance is about 300 ppm of helium. Helium makes up about 23% of the mass of atoms in the universe, with hydrogen making up most of the other 77%. By particle number, however, it is only about 7%. Thus, ³He nuclei are about as common cosmologically as deuterium, and it can likewise be found in gas clouds, newborn stars, and gas giant planets.
The next useful fuel would be lithium. There are two relevant isotopes, ⁶Li and ⁷Li. ⁶Li, the rare isotope (about 8% on Earth) can be fused in potentially useful reactions with deuterium or ³He. Alternatively, both ⁶Li and ⁷Li can be reacted with neutrons (produced in other reactions) to form tritium and helium. This reaction has been used in hydrogen bombs; neutrons produced from the fission igniter and the initial fusion reaction react with a lithium plug to form more tritium, which will then create even more fusion with the deuterium. ⁷Li is primordial, although with a much lower concentration than ³He or deuterium. Thus, it can be found in dust clouds and newborn stars. It is also in gas giants, but since it is a solid at the cold temperatures that characterize the outer atmospheres of gas giants, it sinks into the middle. I'm not exactly sure what process produces ⁶Li, but I will assume it can be found wherever ⁷Li is found, just in smaller quantities.
Finally, if you have some very fancy tech that can compress gasses more effectively than the core of a star, then maybe you just want protium. This is the fuel used by the sun and other main sequence stars. However, even in the core of the sun, the reaction goes quite slowly, with the average power density lower than that of the human body. Protium is the most abundant atom in the universe, and you can find it in gas clouds, planets, and stars.
The easiest place for a starship to get fuel, is probably to collect it slowly as you travel through interstellar space, especially within molecular clouds and nebulae. For one thing, you are already travelling there. The only disadvantage here is that the density is quite low. The densest part of molecular clouds may be up to one million molecules per cubic centimeter, and young planetary nebulae are similar. One million may sound like a lot, but keep in mind that a gas at standard pressure and temperature has on the order of 10^19 molecules per cubic centimeter. Remember we had about 25 ppm of deuterium and ³He, so that means at one million molecules per cubic centimeter, we can expect to find a couple dozen molecules of each. If you can scoop them up efficiently from a wide area around your ship as you travel long distances through the cloud, e.g. using a bussard ram scoop, this could get you a lot of material.
Alternatively, as mentioned in evil professeur's answer, gas giant planets are a much more concentrated source, and are much safer to be around than stars. Regarding the question about gravity, the gravity at the surface of a smallish gas giant, such as Saturn, is about the same as that of the Earth. Keep in mind, there is no actual "surface" on a gas giant, but the depth where the atmospheric pressure is 1 bar, about the same as that of the Earth, is considered the "surface". On Saturn, the temperature at this altitude is 134K, or -139°C. At this temperature, the gas will be about twice as dense (number of molecules per cm³) as Earth's atmosphere. Saturn is composed of about 96.3% hydrogen, with the balance mostly helium, so protium is easy, and deuterium and ³He are available as long as you can separate them from the bulk gas. As I said before, lithium will sink to the center of the planet, so it will not be accessible.
Heavier gas giants, like Jupiter, have greater gravity near the 1 bar level; for Jupiter, 2.5g.
Aside from the lack of lithium, gas giants do not shine, and so locating them from far away can be difficult. Still, with our observational capabilities, we have started to find them by the hundreds around nearby stars, and they seem to be quite common.
Ocean/icy planets and moons
Ocean planets, like Earth, can be a reasonable source of lithium and deuterium, and of course protium. All can be processed from seawater. However, they are generally quite poor in helium, especially ³He. Lithium and deuterium, as well as all nuclei heavier than helium, are relatively enriched on Earth, and presumably other terrestrial planets, compared to the cosmos as a whole. That's what makes them terrestrial planets!
Icy worlds are similar, with hydrogen (and therefore some deuterium) as a component of the water, ammonia, and methane which make up the surface ice, as well as any subsurface oceans.
Surface gravity of ocean and icy planets varies with size, but they have the advantage that you can land on them while you do your fueling, instead of needing to expend energy to "fly". All of the relevant bodies in the solar system have surface gravity equal or less than that of Earth.
Detecting ocean and icy bodies from interstellar distances is even harder than detecting gas giants. Ocean planets may (or may not) be quite rare, but if our solar system is any indication, icy moons are common around gas and ice giants.
Small, cool stars, including red and brown dwarfs, are the most common stars and at least red dwarfs shine brightly enough that they should be easy for a spacefaring civilization to find. Unfortunately they are depleted of deuterium and lithium. Because these are the easiest fuels for fusion, they get burned up first as the star is forming. This is actually the distinguishing feature between stars and planets: the smallest, coolest stars are brown dwarfs, which got hot enough to burn their deuterium, but not to start burning protium. Intermediate brown dwarfs have also gotten large enough to burn lithium. Both red and brown dwarfs are fully convective, meaning that the entire star is well mixed, and all the original deuterium and lithium pass through the core and are burned up relatively quickly.
Stars the size of the sun and larger are not fully convective, and so the outer layers contain deuterium which has never cycled through the core and burned up. However, as other answers have mentioned, the environment near the outer limits of a star is extremely hostile. Although it can be assumed that any starship has fairly extensive radiation shielding to protect it from ionizing radiation, there must be limits to that shielding. The outer atmosphere of stars, although diffuse enough that I don't think there would be too much conductive heating of a spacecraft, are hot enough to emit x-rays, which would be quickly deadly to any unprotected humans. Additionally, the strong, rapidly changing magnetic fields associated with solar flares can in extreme cases be enough to disrupt electronics even on Earth, even inside the protective magnetosphere.
Regarding gravity: The "surface" gravity of a star (or anything else) is proportional to its mass and inversely proportional to the square of its radius. For main sequence stars, which are burning hydrogen in the core, this actually means more surface gravity on smaller stars. For instance the surface gravity of the sun is about 28g, while the surface gravity of Proxima Centauri, a red dwarf with only 12% the mass of the sun, is about 170g, and Sirius A, the brightest main sequence star in our local neighborhood, is twice the mass of the sun but has a surface gravity of "only" 22g. The surface gravity on red giants is much lower, because they have the same mass that they had when they were main sequence stars, but a much larger radius. For instance Arcturus, with a mass only about 8% larger than the sun and a radius 25 times that of the sun, has a surface gravity of 0.05g. With this low gravity, in combination with the strong stellar wind, you might be able to use some very temperature-resistant solar sail to stay in place above the star while gathering fuel. Red giants are also cooler than a main sequence star of the same mass (4300K for Arcturus vs. 5700K for the sun), and so somewhat safer to approach. The red giant phase is a comparatively short period in the lifetime of the star, and so red giants are rarer than main sequence stars; however, their total luminosity is very high, so they are easy to locate. On the downside, near the beginning of the red giant phase, the outer part of the star becomes more fully convective, and so the concentration of easily fusable nuclei like deuterium and lithium will be somewhat decreased.
The outer limit of red giants is even more diffuse than for main sequence stars; depending on how dense you need your fuel to be, you can approach closer or farther. Indeed, at the end of their lives, red giants of moderate mass blow off their envelope completely, becoming planetary nebulae (see above).
Edit: Escape velocity
In my answers above, I talked about the "surface" gravity of different stars and planets. This is the gravity that the starship would have to hold itself up against while it is in the process of refueling from a star or planet that doesn't have a surface to land on. However, this is only part of the problem of gravity; before the ship can match velocity with the "surface" of a star or planet, it would have to lose the speed it gains by going into the gravity well, and after it was done fueling, it would have to escape the gravity well again. This in effect means it needs to pay the escape velocity twice. So, here are the escape velocities of the objects I mentioned. For stars, this is the escape velocity to interstellar space, starting from the "surface" of the star, and assuming that the ship is matching the rotation of the star. For planets and moons, I give both the escape velocity to interplanetary space starting from the surface, and also the escape velocity to interstellar space given the orbital speed of the planet. I don't know if your ship has a futuristic propulsion system where these kinds of velocity changes are trivial, but since you asked about gravity, here it is:
The sun: 615 km/s to interstellar
Proxima Centauri (red dwarf): 577 km/s to interstellar
Sirius A (main sequence star bigger than sun): 655 km/s to interstellar
Arcturus (red giant): 125 km/s to interstellar
Saturn: 25.7 km/s to interplanetary, 29.5 km/s to interstellar
Jupiter: 47 km/s to interplanetary, 52.6 km/s to interstellar
Callisto (an icy moon of Jupiter): 5.9 km/s to interplanetary, 11.3 km/s interstellar
Titan (an icy moon of Saturn): 4.7 km/s to interplanetary, 8.5 km/s interstellar
Earth: 10.7 km/s interplanetary, 23 km/s interstellar
Molecular clouds and nebulae are already in interstellar space, so I won't calculate any escape velocity for them.
As you can see, stars have deep gravity wells, but red giants are again the best bet, because you don't need to come so close to the center of mass.
For gas giants, it would be most efficient to choose a light one far from its star (e.g. more Saturn than Jupiter), unless the ship is stopping in the inner stellar system anyway.
For icy moons, choose one far from its planet, and a planet far from the star. Icy minor planets and Kuiper belt objects would have even smaller escape velocity to interstellar space, but they are less likely to have a molten subsurface ocean, because they are not heated by tidal forces. So you would have to dig your fuel instead of pumping it. They would also be substantially harder to detect, even from within the system.
If your ship uses magnetic fields to pull in fuel, then you need your fuel to be ionized. This rules out gas giants, molecular clouds, and icy/ocean planets/moons. The photosphere (aka "surface") of cooler stars is also largely unionized. However, the stellar wind is ionized, and will be densest a short distance from the star. Planetary nebulae also tend to be ionized, at least when young.