Don't breeze by the Tetons without a visit. The view from Jackson Lake Lodge is awesome. I don't know about trailer camping around there, but I would try to spend a night somewhere around there. Skip Jackson if you need to. About 2 hours is all you need to get your fill of it.
The Cody museum mentioned earlier provides many hours of entertainment.
Personally, I think meeting Cheyenne is a pretty big "must see" in Wyoming. That and stop and eat (burgers) in the smallest, out of the way places you can find. If you do meet him, don't let him see your knife.
