Without a car, you won't go far. I-90 is the sole interstate in the region, running east-west, skirting Black Hills NF and Badlands NP to the north, and passing through Rapid City. It goes on to Sioux City in the east, and west to Wyoming to connect with I-25, which leads south to Denver.
Drive through "Bear Country USA", a "drive-through zoo" containing many animals you otherwise would not want to be in proximity to.
Hike or at least check out the incredible Badlands.
Ride down Highway 16, off of which are conveniently located many of the area's numerous attractions.
Tour the local highways, which can be very scenic in nature.
Visit and enjoy Evan's Plunge in Hot Springs, a mini-water park fed by hot springs.
Visit the area's most famous attraction, Mount Rushmore.
Visit the Mammoth Site
Watch the Old West Shoot-out in Hill City
Horseback riding and camping  soak in the beautiful scenery in the heart of the Black Hills.
The Alpine Restaurant in Hill City -- Dinner menu is limited: Small or Large Filet Mignon. Be sure to save room for dessert!
The Hitchrail Bar and Restaurant in Pringle -- See a true small town watering hole.