+1 to what Robb said.
I took my, then 12 year old, son further out in Eastern Wyoming on a left-over tag. We saw lots of small bucks, but he ended up killing a very nice one, which was his first big game animal. We had an absolute blast and he was hooked on hunting after that. I can't think of a better way to cut a 12 year old's hunting teeth!
The odds of drawing seem to be better the further East you apply (the middle south part of the state "red desert" has the worst odds). Good luck!