My favorites are (in no particular order)...
Lewis & Clark Caverns (Interesting easy walk through a cave system)
Bannack Ghost Town (The best preserved ghost town in the world)
Museum of the Rockies (In Bozeman-best T-rex and triceratops fossils and other exhibits)
Virginia City / Nevada City (Old west towns and Montana's second territorial capital - Bannack was first)
Phillipsburg (Fun small mining town with giant candy shop and rock shops)
Garnet Ghost Town (Interesting ghost town with rich mining history)
There is so much to see in Montana between YNP and GNP. Do your research and find some places that sound interesting to you. Enjoy your trip!