Springfield pretty much has that region covered when it comes to traveling shows; while I was attending MSU, I saw The Beauty and the Beast, Shrek: The Musical, and more. They've even gotten Wicked.
For Branson, I'd say a permanent show might be a better choice; like how Las Vegas had a permanent, specifically-built theater for Phantom of the Opera. Like, I know that if I wanted to go see a Broadway show closer to home, I could take a train or bus to Chicago, where they have more permanent theaters for stuff like that.