SD laws are pretty few and short. No carry in K-12 school property, in courthouses, and while CC'ing, in places that make more than half their money selling booze for on site consumption. (Strangely, the law does not prohibit open carry in bars!).
The one thing that might trip one up is this. State preempts laws relating to possession and carrying. But, several cities/towns have enacted ordinances prohibiting firearms in ANY places licensed to sell alcohol. These ordinances are on the surface illegal, but I'm not aware of any one testing them in court.
OC is legal, as in there's no law restricting it. I just don't see it in Rapid City area at all.
Enjoy your visit!