The Black Hills in June is popular...and can be hot....
WHAT do you want to do and see while you are in the Black Hills??
Have you tried Trip Advisor?
When I go to the Black Hills? I am in a motor home. We have stayed at the Elkridge RV Campground in Spearfish. We love going back Route 14 to Bridal Veil Falls and taking the tour around Custer National Park.
We also go to the Devil's Tower in Hulett, Wyoming (where Close Encounters was filmed all those years ago) and walk around that. Sundance Wyoming has a great RV park with 4 cabins and a great pool. Excellent location too!
Mount Rushmore has a KOA (In Hill City) and there is another campground that has cabins.
Rapid City, SD is a big city and has a lot of choices too.
There is so much to do and see. Good luck!