From Cody you can travel west to the eastern entrance of Yellowstone NP then go toward Fishing Bridge and go south to Grant Village and out the southern entrance and travel thru the Tetons to Jackson. A lot of people go up thru Cooke City and the Beartooth Hwy because of the scenery and then head down the Chief Joseph Hwy to Cody.
I've made that run between Jackson and Cooke in both directions, and the quickest route is right down through the parks. With minimal stops you can figure between 4 and 4.5 hours. Also note that I haven't done that since the road work between the two parks has been in progress.
We drove from Cooke City to Jackson on May 18 2010. It took us most of the day, but we made many stops for bears and picture taking. One stop was several hours. It was a great drive and a great day!
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