The Black Hills in South Dakota deserve consideration (Mt. Rushmore, Custer State Park, and Sturgis, a motorcyclist's mecca). If you can visit Cody, WY on a Friday you'll be able to catch a good old fashion rodeo. Take US 20 west through Shoshone Canyon to Yellowstone's eastern entrance or take State Route 296 north and "do" the Beartooth Scenic Highway and access Yellowstone via its northeast entrance. Give yourself two full days to experience Yellowstone NP. The Interstates from Bozeman, MT to Tacoma, WA are surprisingly scenic so you could "spend" most of your days east of Yellowstone on the way out and reverse it going back. Just keep a journal so you don't forget places you want to visit on the way home. FYI, there inexpensive national forests campgrounds along this route if you are campers.