Custer Gulch, on the east edge of the town of Custer, worked well for us when we were there several years ago for the buffalo roundup in the park. The center spots don't have much shade, but the back-ins around the edges do.
I've not been there, but have heard nothing but good things about Rafter Bar J. It's near Hill City and the turnoff to the road up to Mount Rushmore. The KOA is also on the road to Rushmore.
Depending on your need for hookups, the campgrounds in Custer State Park might be excellent choices.