SD Black Hills tag is 85$ for one bird, AND MUST BE BOUGHT ON THE INTERNET AHEAD OF TIME. Don't go expecting to buy SD tags over the counter but they do sell unlimited amounts for the Black Hills. You can also put in for various limited entry 2 bird praire tags near the Black Hills but mostly private land and no turkeys (or trees for that matter) on the little public land as far as I can tell. I hunt private land on the praire unit north of the Black Hills, don't know about others areas. Someone else can probably give you a better idea on this.
WY tags are otc for one bird and run about $70 or $80 including the required wildlife stamp. Lots of public access on the National Forest but a good map is a must. I have killed birds on the National Forest but most of my luck is on private land bordering the forest.
If you plan on hunting weekends, be prepared for lots of folks hunting on ATVs. Seems to get worse every year. Get as far away from the roads and trails as possible and you might have a chance to be undisturbed. Go midweek and you'll probably be able to hunt without interference. Darn near anywhere up there has turkeys so having an exact spot probably isn't necessary but up around Hulett is a good place to start.