We just returned Saturday from several days in South Dakota, but I don't have much that you may be looking for. We stayed at the Holiday Inn Express in Rap City for two nights, and just ate their breakfast there, as didn't know where else to go, and were surrounded by Denny's and Burger Kings and other chains anyway. We wanted to get out and see the sights.
If you go to Custer, and you should if you are doing Mount Rushmore, we did hit two winners, both easy to find in the small downtown.
One is Burger & Bun, a tiny place, still very busy at 230 in the afternoon. My wife had their standard burger with lettuce, tomato and onion, and everything was fresh and good, very attractive. The burgers are a third pound. I had their buffalo chili, which was also excellent, not overly spicy, and not too many beans. The meat was flavorful, and seemed to be very good quality. It was ground meat, not cubes. Our waitress was terrific. Everybody is right there, it's just one little room.
The other place was even better, we went for dessert -- The Purple Pie Place, recommended to us by friends who go to Sturgis every year. This was a real winner! We had blueberry pie, and the inside was loaded with real blueberries, not a blueberry gel. We loved it.
You can find it easy, it looks like its name -- a two story building painted purple.
If you like German food, our Sturgis friends recommend the Bavarian Inn in Custer. We didn't have a chance to try it, but reviews look good. http://www.yelp.com/biz/bavarian-inn-restaurant-custer http://blackhillsburgerandbun.com/
And, naturally, being out there, buffalo burgers are everywhere!
Other stops were not in that area, Brookings, Mitchell, Wall. We made the obligatory stop at Wall Drug, and yes, it's an overpriced tourist trap, but ya just gotta do it. And this day one of their specials was a Midwestern style sloppy joe, which we could smell right away on walking in, and we both had to have it. They were really very good.
Sorry we didn't eat more, but sadly, our appetites are getting smaller as we get older.
And, darn, I've got to learn to pay attention. I really wanted to try some chislic while in South Dakota, only to learn while in Rapid City that you can only find it in the southeast corner of the state. I could have got some on the way out, but going back was 640 miles, and we wanted to make time. Oh well....
Sorry I couldn't do more for you.