Maybe areas 84 or 87? Yeah there's elk there. But There is a lot of Wilderness area as well which makes access for nonresidents very difficult.Nonresidents can't hunt a wilderness area without a guide. Residents with a license can act as a guide. So if you know somebody in the area to take you in . . . fine. It's been a while, but I remember going up Granite Creek off the Hoback and were in elk quite constantly. I had a cow tag and did fill it, but the boys are where the girls are.

I think if I had to hunt the Jackson/Teton/ Yellowstone area (and there are nice bulls there), I think I would get into area 81. 81 and 84 have fairly long rifle seasons too. About a month. But 81 is big, the critters are there, and there is no wilderness making accessability very easy.

A well kept secret for huge bulls is area 7. In eastern Wyoming west of Wheatland and south of Douglas. Problem with that hunt area is that most of it is private property. Even within the boudaries of the Nat'l Forest. So access is hard as well. BUT . . . there are still a lot of public areas as well as Walk-In and HMA's. These are private lands that the landowner agrees to let public hunting. Area 7 has a very long season as well.
For more info on Private lands for public hunting/fishing:
Go to:http://gf.state.wy.us/wildlife/access/plpw/index.asp