Was just there from May 15 to 19. Second trip. We did Custer State park once again and also the Needles Highway (do not miss that) and Spearfish Canyon tour. We went in mid-May because rooms are about 1/3 what they are now. Stayed at The Lodge At Deadwood, a great place. We stopped at Walls years ago and did not do it again. Just to let you know the 5¢ cup of coffee is not to go. You must get a place in their restaurant area and be served it. I really thought Walls was a waste of time myself. The Corn Palace is not much to see except the building. Underwhelming.
Definitely take the Badlands loop on the way, you can spend quite a bit of time there. Easy a few hours.
Mount Rushmore, we did last time so we didn't go again.
The town itself is fun. I would go to the museum for sure. Give yourself lots of time. We took the bus tour the first trip and it was worth it, it goes all over town and up to the cemetery.
Sorry, this is being typed 3 AM and I was just on my way to bed. Excuse any typos and choppy sentences.

Don't forget the Needles Highway it is breathtaking.