Hanna Campground (http://www.fs.usda.gov/recarea/black...25863&actid=29
Near Lead, SD (Cheyenne Crossing); Forest Services; no reservations, vault toilets, hand pump for water. Small number of sites, but a creek runs right through the campground; I have very fond memories of camping here in our Apache Eagle tent camper.
Custer State Park Game Lodge campground (http://gfp.sd.gov/state-parks/direct...r/campgrounds/
East of Custer in the state park; one of the best state park campgrounds; we have always enjoyed our stays at this CG.
Horse Thief Campground and Resort (http://www.horsethief.com/
Between Hill City and Custer; one of the best private campgrounds we have stayed at; full hookups available
Custer State Park Center Lake campground ((http://gfp.sd.gov/state-parks/direct...r/campgrounds/
Again, east of Custer in the state park; more primitive than the Game Lodge campground, very nice setting
Mt. Rushmore KOA (http://koa.com/campgrounds/mount-rushmore/
This is very close to Mt. Rushmore; we have stayed at some KOAs close to major highways, and while this one is near a main road it is not the typical highway KOA.
Crooked Creek Resort (http://www.crookedcreeksd.com/
Close to Hill City; full hookups are available; close to the Mickelson trail (very nice biking and hiking path on an old railroad grade); the CG has a creek running through it.
Mystery Mountain Resort (http://www.blackhillsresorts.com/
Between Rapid City and Hill City; we have stayed there a few times, but it has probably been more than 10 years ago. It is in a nice location.
There are many forest service campgrounds in the area, and you can't really go wrong. It just depends on what type of CG you are looking for.
You are probably already considering the must-see sites, but also consider:
Driving the Wildlife Loop in Custer State Park (early in the morning or just before sunset)
Hiking Harney Peak
Spearfish Canyon and Roughlock Falls
Badlands National Park (if you have time - about 75 miles outside of Rapid City)
Taking a walk on the Mickelson Trail (near Hill City, Custer or Lead/Deadwood)
There is so much to do in the Hills. Good luck and have fun.