Full hook ups usually mean open campsites. Take a look at Google Earth and switch to satellite view to see what the campsites look like. I do not stay at "camping resorts" because I am more comfortable in smaller, more secluded places. We have camped at Kemp's Kamp outside of Keystone. They are a small campground with some of the sites having full hookups. It is less than 10 miles from Rushmore. Chris' Camp at Spearfish has large campsites with trees for shade but you are still in a relatively open area. Chris' Camp is way up north but a good base to go and see Devils Tower.
While in the area, make sure to get reservations and visit either Wind Cave or Jewel Cave. Both are really nice.
The one thing that I have a hard time doing is to just park somewhere and sit an enjoy nature. I usually try to see everything and miss so much in the process.