Well, with your current plans; Once at the Badlands NP, head south down to Pine Ridge and check out the Wounded Knee memorial. Pine Ridge will be an eye-opening experience.
In the Black hills, Custer State Park is a must up the needles highway to Sylvan lake and out to the Crazy Horse monument.
Deadwood is another nice stay over and the Spearfish canyon area is really nice as well.
Lots of other off the beaten path off road tracks as well, pick up a topo of the Black Hills if that is something that interests...