If they want to travel anywhere beyond their own isolated system, they would either have to figure out how to leave their star behind or to bring it along with them.
One of these problems is much more easily solved than the other. Either way, that civilization would then have no particular use for galaxies as a travel destination.
Couldn't a galaxy be an attractive travel destination anyway, just like a large city can be an attractive travel destination for country folks? Not necessarily as a place to harvest resources, but as a place to go sightseeing and interact with foreigners.
The short answer is no. Space is really, really, really, really big.
Tourism usually requires that you be alive when you finally get there. At that scale, if you chose to visit even the closest galaxy to ours, not only will you be long dead and thoroughly recycled when your vessel arrives, but the passengers that disembark to snap a group photo might not even be considered Homo sapiens any more.
That kind of commitment can only come from existential necessity. Any visitors to a galaxy that came from outside of one would undoubtedly have a technology that allows travel without actually traversing the intervening distance.
You're assuming that those lurking planets harbor forms of life that even remotely resemble us.
Imagine an alien lifeform with an average lifespan of several million years, perhaps the size of a mouse (not much mass) and with extremely slow metabolism (not much supplies needed for travel). For them, traveling to a nearby galaxy at relativistic speeds (only a few years from the traveler's perspective) might be seen as little more than a nice long vacation. Sure, a dozen lifespans might have passed by the time they get home, but maybe they don't care because they don't have children like we do and their civilization doesn't change much. "They released the Galaxy S9 already? That's crazy! Three new models in a billennium!"
You don't even need FTL transportation if you can afford to spend a few eons strapped to a seat.
Why spend eons strapped to a seat, fixated on your destination, when you can play shuffleboard on the cruise ship while you wait? You are just re-describing the first of my two possibilities--the species so well-adapted to space travel that they never actually need to stop anywhere.
And if they don't need to, they probably won't. If you lived in the country, and wanted to visit the city, you might do so frequently if the trip cost you 15 minutes and $10. You might never do it at all if the trip took 50 years and $100billion.
Space travel is more like the latter than the former.
If, on the other hand, travel to anywhere on Earth cost you 1 second and $0.01, you might just visit every city. That's why I say that any non-galactic visitor to a galaxy is more likely to have a kick-ass travel technology. It's a purely time-based argument, and has nothing to do with any property of the species that has it. They would simply spend far more time at their intended destinations than traveling between them.
One of these problems is much more easily solved than the other. Either way, that civilization would then have no particular use for galaxies as a travel destination.