While their family farm was in Kearney, Missouri, they certainly moved out of the state when being chased by the law. WikiPedia does a pretty good job of tracking their robberies in at least 10 states and it's mentioned Jesse moved to the outskirts of Nashville Tennessee after their mother was severely injured by a bomb (a 9 year old boy was killed) detonated by law enforcement trying to capture Jesse.
There's a lot of info available just on WikiPedia alone.
