My wife and I did this 10 years or so ago and are taking the kids this time, we are driving.
Day 1 Sioux Falls SD - Falls Park, SculptureWalk and the arc of Dreams
Day 2-3 Rapid City, SD - Badlands NP, Custer State Park, Wind Cave NP, Mt Rushmore, Crazy Horse, Deadwood, Jewel Cave NM, Minuteman Missile NHS.
Day 4 - Billings, MT - Devil's Tower NM, Little Bighorne Battlefield NM,
Day 5-9 - Yellowstone NP & Grand Teton NP
Day 10, long ride home.