Plan to spend a few days in Cody. The museum takes 3 days to see properly. Take a long day trip to Red Lodge, MT and see the Bear Tooth Pass and on the way back to Cody use the Chief Joseph trail. If you go Cody, YS, Jackson you will go through Teton National Park. I don't know how you'll come into the state, but if you come in through the Black Hills, you must go to Devil's Tower. After Jackson I would go out through Dubois and the Wind River Valley. If you have the time there are some fabulous drives and hikes around Dubois plus great trout fishing in the Wind and it's tributaries. Stop at the National Bighorn Sheep Interpative Center and they will give you directions. Tell then Dave and Barb sent you. WY is one of my favorite states, there is just so much to see. A few more; Thermopolis hot springs and dinasaur dig, The Wind river canyon, Sinks Canyon near Lander, Hoback Canyon south of Jackson etc. I hope you have lots of time because there is a lot to see, take your time and have fun.
