I would recoomend either Harding County (NW SD)or Fall River county (SW SD). Both have a bunch of public land. I would say Harding has more public land and more deer and antelope but it also has more archery hunting pressure. When I 1st started bowhunting out there it was a novelty for those ranchers to see a bowhunter. Nowdays if you go into the bar/restaraunt in Buffalo (Harding County) in September you are going to run into a bunch of bowhunters from all over the country. Go to the SD Game and Fish website you can order a free atlas that shows public land. If you are going to hunt Fall River County you are going to want to pick up a grasslands map also. If you can figure out who owns the private land it is not too tough to get permission to bowhunt antelope although deer is usually another matter. There is plenty of public land so you should always be able to find a spot to hunt without being on top of someone else.
Dan