I don't think you are going to find a "Resort" type RV park like you are describing. When we were there last year over the 4th of July, we traveled around the area and didn't see any RV parks that were more than a parking lot with with hook-ups. Inside Custer State Park, there are some really nice and woodsy campgrounds, but getting one of those is like harvesting gold from Fort Knox. You'll need to reserve a site way, way in advance.
We stayed at Buffalo Ridge Camp Resort which is a Good Sam campground:
Click here..
The sites are fairly close to each other, but you do have enough space to get slides out and awnings out. They do have some really nice amenities at the park, swimming pool, cabins, laundry facilities, TeePee camping, camp store, playground for kids, the train ride, tent camping, RV camping, and the theater. It's a large park and if you have kids, they will have fun, especially with the playground and pool.
If you are staying anywhere near the Mt. Rushmore area, you won't be spending much time at your campsite. There's just so much to see and do and explore, every minute you spend at your campsite and not exploring the Black Hills, Deadwood, Sturges (yea... Full Throttle Saloon), Custer State Park, Mt. Rushmore itself, thousands of local attractions, restaurants, shops, events, and the miles and miles of fantastic scenic routes through the mountains and hills, you'll be too exhausted to actually "enjoy" your campsite. So, simply pick a spot to "park it" and use your camper as a bedroom from the night. You won't be there very much.
If you don't like this one, here's a link to a list of campgrounds that you might find helpful:
Click here.
