We stayed at the KOA at Interior SD which is at the south entrance to Badlands. Great park, at the time, but I think I saw they jacked up their prices sky high maybe to $59/night so you need to decide if that's worth the price. Scanning around I see one CG in Wasta with one review but a good one. There is/was a GS park in Wall but it's closing. A couple other around but with bad reviews.
We did a lot of hiking in Badlands, spent a week that time and have been there a couple of times. Saw Interior VFD put on a fireworks display for the 4th that Moe, Larry and Joe would have been ashamed of...heh. But they had just had record rainfall. Wild flowers everywhere.
Good luck with Custer it's usually hard to get in but this late you might succeed there are a lot of cg in the area tho. No comment on Deadwood never been and don't see that changing.
Last couple of times we went thru we stayed at Hot Springs. Go to at least one of the two caves, you need to get there early to snag a tour
RV Trip Wizard shows all this stuff you may want to look.