RE: Elk Tag Lotteries
Haven't heard anyone mention South Dakota yet, I'll share my experience with that area since that's where I've done all my elk hunting, in the Black Hills region.
You apply online just like Wyoming, you pay the price of the tag and check online to see if you got drawn. If you didn't, you get a refund in the mail.
I always hunted the experimental forest area, around HWY 385, kind of between Silver City and Rochford. There's a ton of elk in that area, just watch out for mountain lions.