A little math shows the relative velocity in which you travel one light year measured in a rest frame, in one year in your spaceship's frame, is 70.7% of the speed of light.
If you happened to be moving at the ludicrous speed of the "Oh-My-God" cosmic ray recorded in 1991, it would take you three seconds of your time to travel to the center of the galaxy.
That should be good enough for anyone!