We did exactly what you are planning by camping at Angostura Recreation Area, a SD state campground on Angostura Reservoir SE of Hot Springs. We had a beautiful, well-maintained, paved site on top of a hill with great views of the lake and Black Hills out our rear picture window. New restroom building with showers and reasonably priced for a campsite with hookups.
After staying there, we moved to the Sylvan Lake cg, part of Custer SP, to see Mt. Rushmore, Jewel Cave, the buffalo and donkeys, and the Needles Highway. However, if I had known then what I know now, I would not stay at Sylvan Lake again--very tight, small sites and no dump.
PS--When we went to Voyageurs NP, we stayed at Birch Camp located just west of International Falls. For more info on it, see my review on RVParkReviews.com.
