We spent 10 days in Yellowstone and Grand Teton, and let me tell ya, i wish i'd had more time there. the entire place is beautiful, the geysers impressive, and the wildlife...well, we had a rather large grizzly within a couple hundred yards of our doorstep at one of the onsite hotels while we were in yellowstone, and also saw a buffalo "gore" the car behind us. not to mention the moose, elk, eagles, etc, that are EVERYWHERE. Try to work in a raft trip, and don't be afraid to take some of the NPS tours because you get off the beaten path (really) and they will show you some areas that no one else gets to see. Favorite area? the valley and the areas right around old faithful. have fun and take your time!
Edited to add: i will second attending the museum in Cody.