For something non-touristy~definitely take a drive through Spearfish Canyon. You can get out and hike part of it, too. They have maps with instructions that'll get you way back in there so you can admire the sound and the freshness of their beautiful waterfalls. There is a creek that runs through the Canyon and it is just so nice there. Of course, there is no charge for it because it's just part of the nature in the Hills area.
I also like to hang out in Keystone. It's just the cutest little town at the bottom of Mt. Rushmore.
You could also drive over to Interior and go down through the Badlands. They are beautiful and pretty unusual.