Also look up Black hills Hunting lodge. Located in the heart of the black hills. Nice cabin feel with all the best trails right out of the drive way. Great people and they know the hills better then anyone! Very affordable and definitely the most unique place I’ve stayed in the hills. I most definitely will be going back very soon!
We go almost every summer and stay near Hill City at the Rafter J Bar. It is a nice campground with all the amenities. You will need to get an OHV permit for riding on the roads, they are easy to get through different counties, it's a really cheap. To use the Black Hills trails you'll need a Black Hills Trail permit on top of the OHV permit, they are available at many gas stations, visitors centers etc...I finally licensed my RZR in SD so I didn't have to get the OHV permit every year and for the other states that it is reciprocal in...
There are hundreds of campgrounds in the Hills. A great all around campground is the Palmer Gulch KOA near Hill City. I live about 3/4 of a mile from it. Has trails out the back and has about all the amenities you could ask for and very reasonable rates for what you get. If you want more of a boonedocking experience there is a little BH Forrest camp ground in the middle of one of the best trail systems called Ditch Creek. The campground is called Ditch Creek Campground and it is just south of Deerfield Lake. Dozens of awesome trails right out of the campsite. Not far from there is an old silica mine that you can actually drive an RZR into.
Awesome place, we actually go at least once a summer and sometimes twice a summer.
Another decent campground that wasn't mentioned is Mystic Hills Campground which is just south of Deadwood a few miles. It's right at the base of Custer Peak and you can pretty much ride in any direction from there. With being close to Deadwood, you also have some night life and some good places to eat.
As far as the SD trail permit, just order it online before you leave, it's easier and you don't have to run around looking for a place. Plus, you can put it on a clean machine exactly where you want instead of slapping it on in a hurry.
If you are looking for a great place to ride, seriously consider it !!!