Seeking round trip advice from Minneapolis to Yellowstone

I work at Custer State Park. The time you have listed for your trip is right during the Sturgis Motorcycle Rally and it is one of the busiest times in the Black Hills. Mt. Rushmore, Crazyhorse, Custer State Park will all be very busy. You may want to consider arriving the 2nd week of Aug to avoid all the crowds, especially if you don't like motorcycles, the roads will be packed with them late July and then first week of Aug.