When I was looking.. I had children with me and I was looking for a rustic type place, with some amenities for the kids..
I ended up staying at Beaver Lake Campground (Beaver Lake Campground | Beaver Lake Campground, Custer, South Dakota
)... It was nice.. nothing to write home about.. but it was clean, reasonably priced and the water-slide provided some entertainment for the kids after a long day of site-seeing..
Also, we stayed a couple years ago at North Stockade Lake Campground in the park.. LOVED it.. but we only stayed a couple days.. only draw back for extended stay is limited hook-ups.. if we would have stayed longer, we would have had to tear down camp to go get water and dump.. and that's no fun..
Finally, I didn't stay at Custer's Gulch.. but I did rent a car from them.. It looked to be a very nice place and close to the park entrance...
Good Luck !! its a beautiful place to visit.. we are going back to that area beginning of August... Sturgis... have fun !!