The Badlands are interesting. Just be sure that you ignore the millions of billboards and stay far, far away from Wall.
I don't know if you want to spend a day mountain climbing, but
Black Elk Peak (formerly Harney Peak) in the Black Hills is the highest point in South Dakota, very close to Mount Rushmore and
a relatively easy hike for a mountain climb. When we went, we started off in mild, sunny weather and experienced hot, dry patches, rain, snow, and terrible pockets of humidity on the way up, then were hailed on at the top

. It was all worth it for
the view. You can see into four states from there. A nice soak in the
Evans Plunge natural hot spring pool is nice afterward, provided it's not packed with people.
I also wasn't very impressed with Mt. Rushmore, but it's still a must see. Crazy Horse is much more impressive IMO, but I don't think they are ever going to be done with it. There are a lot of great hikes and some nice little museums in the area; there's plenty to do if you are interested in that sort of thing.