Howdy, I've done the Mount Rushmore thing a few times from Michigan. We normally take I 90. There are places like the corn palace and several other well known spots to see. We've always stayed at Custer State park but you need to make reservations early if you want a good spot with electric.
I always carry a 5 gallon can of diesel when going out West as there are plenty "no service" sign along the interstate. There isn't any real hills till your get to the Rapid City area so towing with a decent TV isn't a problem.
The Black hills are fairly steep but doable even in a medium grade TV.
We normally go to the International peace garden when in the Dakotas and to Terry Roosevelt northern park. We stay at Red River Campground and take in the amp. theater good fun family stuff.