This video explains the limits on how far humanity can go in space, assuming that we never figure out FTL but are restricted to sublight speeds. You might at first think that we should be able to go just about everywhere, even though it might take a ridiculously long time to get there… but you’d probably be wrong. In short, the Local Group of galaxies is gravitationally bound together, so we should be able to go where we like among the nearest hundred trillion or so stars. But the more distant groups of galaxies? The expansion of the universe is not only moving them away at a good fraction of the speed of light, that rate of expansion is increasing. A sublight ship might be capable of reaching speeds faster than the current rate of recession, but the starship will not be able to catch up with those distant galaxies as they accelerate away. At some point in the distant future, the other galactic groups will have receded so far that no light from them will ever make it here, and the skies at the edge of whatever remains of the local group will be utterly dark, without even cosmic background radiation. Some far-future observers will look out into the universe and see nothing… and so they won’t see evidence of the expansion of the universe, and thus won’t understand anything about the Big Bang. For them, it really will look like the universe is eternal and static.

Best to get on that hyperdrive program, I guess.