When I travelled East through Montana back in 2004 I branched off of I-90 just East of Missoula and took 12 to Roundup, then branching South to see the Little Big Horn Monument. I think Montana is the road kill capital of the U.S. so keep your eyes out for animals, live and otherwise. Little Big Horn was worth the time.
Another highlight of that trip was Devil's Tower, which is not too far from LBH. I wasn't expecting much, after all it's just a big rock, right? But it really was impressive in person. There is camping there, but there are also places to camp not far from there that would be better.
If you have the time make a run through Yellowstone. Entering from Cody to Cooke City via Dead Indian Hill Road and Chief Joseph Hwy is awesome for either entering or leaving the park. Very steep with switchbacks, but the views are incredible when coming from the East. I spent one night at Buffalo Bill State Park before taking that route - it's very convenient for an early morning start to roam through the park.