If we can put a spacecraft in orbit around a star with unusually high velocity relative to the center of the galaxy, then it can travel long distances "for free", and have a long-lived source of power. The time scale will still be at least millions of years, so it will have to be a very long lived spacecraft.
Need gravitational slingshots to insert into orbit, or else accelerating (and decelerating) will be just as difficult as achieving the high speed without a star.
Kapteyn's Star is heading away from us, so we would have independently achieve velocity fast enough to catch it. This seems like a bad idea. Barnard's Star is coming towards us.
Tagging along with a hypervelocity star allows exploring beyond the galaxy.
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