It's a beautiful area, with mulies, elk, whitetails, turkey, antelope and some great fishing. The Bighorns are right there, so lots of national forest. BLM to the East and South.
All private from the base of the mountains, out past the river bottoms. Be friendly, make friends, help a few people out. There are worse places to go.
As for DUIs... Most of Wyoming has significant problem.