I'd like to add a few more good things for South Dakota in the Black Hills area.
See the things mentioned by eschwarz above, all east of Mt Rushmore. Then exit Rushmore to the south and take the Iron Mountain Highway to the west. The pigtail bridges are cool, and the views from along that road are spectacular. This will take you out near the Crazy Horse monument. Rushmore pales in comparison. I highly it.
Head further west and tour the Cave of the Winds. Amazing stuff!
The only bad part about doing this is having to drive across Wyoming -- And I don't mean to slight our least-populated state! It's just a really boring, flat drive until you get to the western portion, around Jackson and Yellowstone.
If you pick up a AAA map of South Dakota it has the most scenic drives laid out for you.
RAD