Here is a 2nd vote for the KOA in Hill City (https://koa.com/campgrounds/mount-rushmore/
). They have a nightly bus to lighting ceremony at Mount Rushmore that is a must do. Also, consider going to the Crazy Horse Memorial, if you are into Indian History (this is better the then the Smithsonian American Indian museum in DC).
I recommend you sign up for the KOA membership card it you stay at a lot of KOAs. You get a 10% discount and can earn free stays for only $30 per year. If you have the Allstate RV towing insurance membership is free.
Another campground we like was Whistler's Gulch in Deadwood (Home
). They used to have a trolley that would take you downtown for a couple of bucks so you would not have to fight for parking and can enjoy some adult beverages. Whether you drink or not, you have to to go to Saloon#10 where Wild Bill Hickok was killed when holding the famous Aces and Eights hand while playing poker.
Have fun!!!!! The Hill City and Deadwood area is one of our favorite trips.