South Dakota leases vast areas of private lands for hunters. No kidding. Check the the state website for "Walk In" maps and rules. There are some very good antelope areas in Fall River County and Harding County.
Buffalo Gap Nat'l Grasslands is public land. Buy your map from USDA Office in Wall, SD.
Good antelopin' to you!
Fire up the grill! Deer hunting IS NOT catch and release.