We spent 2 weeks there the last of July and stayed at Custers Gulch RV Park. It is between the town of Custer and Custer State Park and close to all the other attractions. The sites are very spacious full hook up w/ gravel pads. Sites 19-23 were the best in my opinion as they offered the most shade.
The owners were very nice and take great pride in their park.
http://www.custersgulch.com/
Rafter Bar J is also very nice and we have stayed there in the past. We didn't return there this time strictly because of the cost.
I second the suggestion on the Alpine Inn. Hope you enjoy your visit, it's a nice area.