There are a lot of good places to hunt. You can get a map of public hunting ground from the SD Game and Fish. Start there. I would look from Mitchell to Winner. There are quite a few public areas between the two and all are good hunting. If you come mid to late season you won't have much problem with other hunters.

The first 3 weeks of the season are really crowded. After that its not bad at all. You should be able to find plenty of places to hunt and plenty of birds as well.