SD State Parks and Rec Areas If state park or state rec areas don't exist where you want to go, there are lots of other options.
In many communities large and small, look for the bright orange "Rooster Rush" signage. The local bank or bar can suggest where to stay (bankers usually know farmers who allow hunting, too). Many small towns have a muni/county park with camping spots. Motels often have a few RV spots, too. Public lands where hunting is allowed might not have a parking area, leaving hunters to park in the ditch or along the side of a gravel road.
During opener, a lot of small towns have community suppers (full on roast beef dinner and homemade pie for $8), early breakfast and dinner specials at the town café, 5 AM church services, and lodging/camping that is only open during hunting season. There are also fall festivals, craft shows, other events for non-hunters.
We'd be glad to have you in South Dakota! Safe travels!