Rapid City
I have stopped in Rapid City 3 times on the way home from OSH, each time with a different set of passengers.
Car rental on site at KRAP and a short drive to the city and Best Western Ramkota Hotel, rustic, very nice and a good restaurant is part of the hotel as well.
Rapid City is a very interesting town with all its bronze presidential statues and a well documented history.
Mt Rushmore is a 30 mile drive and there are many options if you have time to stay a couple of days. Crazy horse, Custer state park and much more.
Mt. Rushmore has its own advisory frequency and helicopter sightseeing traffic is ever present. The black hills and surrounding geography reminded me of growing up in Switzerland and it is truly a shame to include that scenic state in "flyover country", Stop over would be more appropriate IMHO.
There are less expensive options and more rudimentary accommodations but my vacations are short and few, so I allow for a bit of luxury when I do get to travel.