Depends how much time you have.

I'd say that Yellowstone and the badlands are must-sees. Mt. Rushmore is very underwhelming; far more impressive is the Crazy Horse monument several miles down the road.

If you have time, I'd strongly recommend 2-3 days in Chicago. I would suggest taking the northern route from Bozeman (I-90), which will take you through the badlands, Mt. Rushmore, and Crazy Horse, and to Chicago. It's more interesting than the southern route through Kansas City, St. Louis, and other un-noteworthy places.

If you really want a taste of Americana, stay off the interstates as much as possible. It will be a much longer drive, though.