I don't think you even need generation ships, if you can maintain a constant acceleration. And with constant acceleration, going to our nearest potentially habitable neighbor isn't that much further, subjective-time-wise, than it is to Andromeda.
Assuming acceleration of 1g, from here to Alpha Centauri, it would take 6 years objective, 3.5 subjective. To the center of the galaxy, it would take 27,000 years objective, but only 20 years subjective. Magellanic clouds? 162k years objective, but only 23 years subjective! 28 years to Andromeda.
Fuel may be in short supply, but relativity really works for you - ignoring abrasion and impacts, if you can get to one galaxy, you can get to most others in your neighborhood.
(All calculations derived from http://spacetravel.nathangeffen.webfactional.com/spacetravel..., because I'm too lazy to do it by hand.)
Assuming acceleration of 1g, from here to Alpha Centauri, it would take 6 years objective, 3.5 subjective. To the center of the galaxy, it would take 27,000 years objective, but only 20 years subjective. Magellanic clouds? 162k years objective, but only 23 years subjective! 28 years to Andromeda.
Fuel may be in short supply, but relativity really works for you - ignoring abrasion and impacts, if you can get to one galaxy, you can get to most others in your neighborhood.
(All calculations derived from http://spacetravel.nathangeffen.webfactional.com/spacetravel..., because I'm too lazy to do it by hand.)