There is world class fly fishing not far from there on The Miracle Mile and Grey's Reef. Worth the drive. In Kaycee, just south of Buffalo is the park dedicated to Chris LeDoux, but that is all there is there.
If you are doing a public land hunt in that area I would reccomend taking the first respectable buck you see. By the second week the pronghorn are wary of everything but there will be less hunters out especially mid week. Also, don't count on fishing, check the weather and if the temps aren't too cold you can get some descent fishing for brooks or browns.