We've been out to the Black Hills two years in a row now and would HIGHLY recommend Rafter J Bar ranch in Hill City, SD.
A great campground, wide open spaces, George S. Mickleson trail runs through it, minutes from Mount Rushmore, great pool and playground (we have two small kiddos). The "Ranch Camp" area is the best - great trees. All you can eat Pancake breakfast available in the mornings. We saw a LOT of different campgrounds, and this one is tops! Happy Camping!