On that route you certainly should consider the Black Hills of South Dakota, around Rapid City--Custer State Park, Rushmore, Needles Highway, Crazy Horse.
We stayed out at Red Rock RV Park in Island Park, Idaho which is about 20 miles from the West Entrance to Yellowstone, but a nice drive and also a beautiful area in its own right.
Consider also Colter Bay Village RV Park for a visit to the Tetons. On the way back, consider Colorado. Many great areas of that state, and will be cool in the Summer. Maybe also Taos and Santa Fe, New Mexico.