In South Dakota, the State Parks have a permission policy for caches placed on their properties. Please contact the local state park superintendent to seek permission. If granted, please include a statement about that in the text of any submitted cache pages. The South Dakota State Park geocaching page.
Federally, the Black Elk National Wilderness Area, managed by the National Forest Service is off limits to geocaches. So is the Mount Rushmore area and any other areas managed by the National Park Service.