We just returned from that area. Didn't make Yellowstone due to having to return home for Hurricane Matthew but did visit Wall Drug (tourist tape IMHO, $36 for two burgers, drinks and onion rings), Mt Rushmore, Devil's Tower, Badlands NP and Black Hills NF which were all great.
If your equipment can handle twelve miles of dirt road and your camping style doesn't require amenities, Sage Creek CG in Badlands NP is awesome and free. You just pick a spot around a loop and set up; no designated sites.
Buffalo roaming right through your campsite. Lots of other wildlife as well and just amazing terrain throughout the Park. Most mornings we had one or more of these as breakfast guests
We also spent a few days at Horsethief Lake CG in Black Hills NF (not to be confused with the commercial Horsethief Lake RV Park) and used it as a base for exploring the Mt Rushmore area. Its only a few miles from the National Monument, Custer SP and the drives mentioned by other posters. Highly recommended; View from the back of our site
As mentioned, Devil's Tower is a bit of a drive but well worth it or you can camp at the federal CG there. We had a great view of the Tower from our campsite
Hope you enjoy your time in the area as much as we did.
