Just south of Mount Rushmore National Monument is Custer State Park, home of the Black Hills Playhouse. This is an absolutely beautiful drive through the hills, even if you never get out of your car. Wildlife abounds, including a very substantial buffalo herd for which a round-up is held each fall. Just south of the park is Wind Cave National Park and Jewel Cave National Monument is immediately west.
Immediately north of Custer is the Crazy Horse Monument, an aggressive mountain sculpting project a la Mount Rushmore which continues to take a little more shape every year.
As with much of the Black Hills, one thing is constantly leading to another -- so just simply put Custer State Park on your itinerary and let your discoveries there guide your path. It is some of the finest scenery that the Black Hills have to offer and that is saying a lot.