You may find everything already booked up. With the Bike rally at Sturgis the first two weeks of August, people avoid the area from late July till after the rally and this crowds the bookings the remainder of the summer.
In any case, the Black Hills is a relatively small area. I stayed at Spearfish City Campground on the north end of the BH and rented a car (no toad) and zipped all over the place seeing stuff. Its nice to be able to stay in the middle of things, but it may not be possible to get a site. There are also some Forest Service campgrounds such as
Roubaix Lake Campground on US385 between Deadwood and Hill City, and there are others, such as
Pactolan Reservoir CampgroundMy trip report on my hurried visit to the Black Hills and the Badlands and the eclipse, last August,
HERE.
Charles