I figure every part of the Milkyway galaxy is reachable by then, with a strong feeling that Borg space will be greatly reduced, and relations between ex-warring species has the galaxy on edge. I'd limit the number of warp capable species to make it work, but a ship (which I would name Enterprise G) could be testing out a wormhole-warp engine by then, to seek out newer and stranger species beyond our galaxy.
Our Galaxy is an extremely
big place--and it extends in three dimensions
. When we look at any particular map of the Galaxy, all we see are the largest concentrations
of stars (the core and the so-called arms). There are also stars that aren't visible both above and below the galactic plane because their concentrations aren't as heavy, and as such, they don't glow as brightly together. Our Galaxy isn't so much a flat disk, but a very large sphere with a very visible cross section.
There is potentially about a trillion
star systems in our Galaxy. Even with transwarp or slipstream drive, it could take further centuries (if not millennia) to explore them all. And that's not even counting the countless star clusters
that are within the Galaxy's sphere. Each
of those clusters could contain tens to hundreds of thousands of stars.
Forget other galaxies. Heck, you'd need transwarp drive to really