You are going to have soooooo much fun! I drove from Alaska to Virginia with the monkeys and we had a great time!
Mt. Rushmore is amazing but they don't let dogs into the park itself so I just parked and let the monkeys see it from the parking lot
Sturgis is fun, the Harley shop let the monkeys in to shop, and the Black Hills are beautiful!
Are you planning on staying in hotels? I found that the Holiday Inn Expresses were clean and pet friendly.