Great trip. The badlands and wall can be done from one campground. As can Custer, Rushmore, crazy horse. Have not been to deadwood but it may fall into that not having to move area. We stayed at Sleepy Hollow RV park in Wall. Great spot for both the city and Badlands, while there do not forget the Missile Soul tour.
Stayed at Ft. WeLikit rv park in the city of Custer. Found it to be a great park and well within driving for all that is around that part of SD. Where ever you end up staying make your plans very early as you will be going there in the middle of the season.