Then it would zip past Alpha Centauri in about 3 days, not alot of time to do any serious observation.

I like the slow boat approach, with a twist. There has to be a way to slow down the atomic clock of matter. Relativistic effects are one way - intense gravity for example. But what about supercooling and intense magnetism?

Picture yourself the captain on the Enterprise. You plot a course and give the order to engage the Chronometric Engine. Observers see all the lights wink out aboard the ship as it sails silently to the stars. Seen from the bridge, the stars are moving, shooting past by the hundreds. The whole galaxy is in motion, and you're nearly at your destination. And all you've done is slow down your clock. You've still got lots of fuel for maneuvering (assuming no chemical decay with time), and you can communicate with similarly time-delayed ships in real time over lightyear distances without any causality-violating FTL technology.