Angostura might be a good spot to do both Wind Cave and Badlands NPs. There is a nice RV park in Wall which is 10 minutes from Badlands, and Custer SP would be a very good one to see Wind Cave from, plus it will get you much closer to Mount Rushmore NM. There is a campground in Wind Cave, but sites are small, and there are no hookups or dump. It is very quiet and peaceful.
FYI, while at Wind Cave, drive the back roads. There is much more to that park than the cave. You will see bison (100%, no cattle DNA), pronghorns, and very possibly elk. Also there won't be traffic jams to see them like in Yellowstone.
