The Corn Palace in Mitchell SD is a sight to be seen. Their civic auditorium is decorated on the outside and inside with corn, and it's free. [
link to a photo] We stayed at the Dakota Campground while there.
Just before you cross the Missouri River (headed west on I-90) there's a rest stop with a enormous statue and a museum (also free). [
link to photo]
While at the Badlands be sure to see the Minuteman 2 Missile Museum and silo. You'll have to make reservations ahead of time if you want to tour the command center. The first two are free, there's a charge for the tour.
In the Black Hills we toured Wind Cave; no problems finding it. On our way back to our campsite (Heritage Village Campground, with views of Crazy Horse) we drove through Custer State Park on SR-87. There are some amazing views of Mount Rushmore from there, as well as animals. [
link to photo]
If you have the National Park Pass (what used to be the Golden Eagle) it will get you a discount on parking at Mt. Rushmore and on the NPS tour of the cave; it doesn't work for the tour of the missile command center.
We enjoyed a good (almost) home-cooked meal at the Hill City Cafe (in Hill CIty, SD).
Safe travels.