Your going to LOVE it. Was out there last year 2nd week of Sept at Grant Campground. Sept 15 was last day campground was open before closing for the winter. Best trip we ever took. Make sure you have reservations. We had scores of people without reservations coming up to the ranger station trying to find campsites. Everything was full. Fishing Bridge has full hookups but its more like camping in a parking lot. Grant was much nicer but no electric, water or sewer. They do have a dump station and water though. Generator use is limited. We had 2 inches of snow last few days we were there.
Horse Thief campground was nice near Mt. Rushmore. Highly recommend taking a scenic drive on the needles Hwy.