We visited Custer State Park several years ago the week after Labor Day -- had to fly in and rent a car so we weren't in our RV at the time. We stayed at both the State Game Lodge and Sylvan Lake Lodge, and although you wouldn't be staying there, I recall the restaurants in both of them being quite nice -- not pricey, but good food in a nice atmosphere. Might be worth a try.
I also vividly remember going through the park and feeding the donkeys. They loved the small carrots. Even if initially they're a distance away, showing them that you have a bag of carrots will bring them right to you!