My sons and I were at Yellowstone on July 4th, had a great trip in the camper. It was not as crowded as previous trips, for instance there were open spots in the Fishing Bridge RV park.
I would recommend stopping off for a day at the Buffalo Bill Historical Center in Cody, they have a tremendous gun collection and a fascinating set of exhibits - can easily spend a full day there. At the moment they have a really nifty display of paintings about the Lewis and Clark expedition, made by a talented guy who went along the route and "imagined" what it must have been like. He drew from the actual scenes that were discussed in the L&C journals, and the paintings are magnificent.
On the way west out of town, they have a tourist-trap type frontier town, which is a bit more than meets the eye. The buildings are all original historic cabin structures which were dismantled and moved to that spot, including a saloon and the cabin where the Hole in the Wall gang used to meet. More interesting to me is that it is now the gravesite of Liver Eatin' Johnston, famous mountain man and the inspiration for the "Jeremiah Johnson" movie.
Inside the park, you can wear yourself to a frazzle trying to see and do everything. Your first trip will involve a lot of driving in order to see the sites. After you've looked at enough smoking holes in the ground to satisfy you, and seen the geysers go off a few times, take advantage of the trails and other opportunities to get away from the crowds - horseback rides, picnics, etc. and you will have a great time.
On the way back to Arizona, you could wend your way down to Thermopolis and spend a day soaking at the world's largest mineral hot springs, and if you have any kids along they would get a kick out of visiting the Wyoming dinosaur center that is close by.
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