There aren't any campsites in rest areas along the way, though they make dandy stops for lunch. The rest area by Chamberlain, SD is an interesting one & has some neat displays on the Lewis & Clark expedition - worth a stop for lunch or just to stretch your legs.
We prefer to spend the night in campgrounds, and SD is loaded with KOAs which are fine for overnighting. We've been to nearly all of them over the years. That said, We liked the Jellystone in Sioux Falls and LOVED the Rafter J Bar when we stayed there years ago.
I second the recommendation to take the Badlands loop drive. It's quite do-able while towing, though you may find parking spaces for longer rigs at a premium if you want to stop for a hike. (It will be HOT there in the summer.) You can see plenty of the badlands scenery from the road, however. Should you want to spend the night, we really liked the KOA several miles south of the Badlands - nice shade (welcome in that area) and close enough to be a good base for sightseeing. Quiet there too (unless you're there during the Sturgis rally.)
Lots to do in the Black Hills. We filled a week, easy. Don't miss the Crazy Horse memorial.
