We've had a good run out here in the boonies of the Milky Way, but as a civilization, we're starting to mature a bit, so maybe it's time for us to move closer to the center of our galaxy where things are really hoppin'. One option is to look for a new home somewhere more exciting, but we could also just pick up and move our entire solar system instead.
Stars like our sun easily produce enough energy to move themselves, it's just a question of finding a good way to efficiently harness and direct that energy. One such method of doing this is what's called a Shkadov thruster, which is essentially a solar sail that so big that I'm going to invent a new adjective to describe the size of it: "stupendoginormous." Yes, it's that big.
A Shkadov thruster is big enough to capture and reflect about 50% of the light emitted by the star that it's built next to. It's able to harness enough light pressure to balance the gravitational attraction of the star, allowing the sail to "hover" above the star without needing to orbit like a planet. With the sail in place, there's now an asymmetry in the overall radiation pressure that the star is emitting, and all those photons not running into the sail team up to generate an infinitesimal amount of net thrust in the direction of the sail itself.
By "infinitesimal," we're talking a speed of 45 miles an hour after a million years, but the thing about small amounts of constant acceleration is that if you wait long enough, it all starts to add up. After a billion years, a star like our sun would be zipping along at nearly 44,000 miles per hour, and by that time it would have traversed 34,000 light years, or about a third of the width of our galaxy, dragging all of the planets along with it.
Creating a stellar engine like this would, to put it mildly, not be easy. Optimistic projections suggest that our species may have the capability to do something like this in a few thousand years, which gives us plenty of time to figure out which direction we want to head in.