We could launch a vessel to Proxima Centauri right now that would arrive in thousands of years. If the passengers have lifespans measured in millions of years, that's comparable to a month for someone who lives 80 years.
Has a method of long term stasis been found yet (like you see in Interstellar or other movies) where you can nap and be kept alive for that long? Otherwise I think you'd still need to overcome the mental limitations of being stuck in a metal tube for thousands of years with no way out and no way to pass the time. Or at the very least, some way of staying asleep for a few years--wake up for a few months--sleep for a few years--wake up for a few months and so on.
My guess is that stasis would be feasible sooner than keeping people fully alive and awake for the whole journey. In the latter case, they'd probably spend most of their time in the holodeck. Either way, on the scale of the universe, living in a metal tube is not very far removed from being stuck to the surface of a small iron pebble as we are now.
