The Mt. Rushmore KOA is an excellent campground to stay at (especially if you have any kids--still a good campground without the youngins). Its only a few miles down from the monument (and I think it even has a bus service that takes you there).
We've stayed there a couple of times, the last time was a few years ago, however. Looks like its still a decent campground given the reviews on rvparkreviews:
Mount Rushmore KOA - Hill City, SD - RV Park Reviews