Best route from Cheyenne WY to Coulter Bay (Grand Teton) WY

I would second, or third, the US 287/US 26 route. I like the fact that portions of US 287 follow the old Oregon-California Trail, the views after Lander are better than US 191, and the route is the most direct from I-80 to Colter Bay. However, if you have never been to Jackson and don't have time to take a side-trip there while at Colter Bay, I would recommend using US 191 just to see the Jackson area.