Yellowstone is a nice ride. I toured through there on my way to Alaska last summer, at the height of the tourist season, and wasn't impeded by traffic whatsoever (either inside or outside of the park). We came in from the Cody/Thermopolis in Wyoming side to the east - really beautiful ride through Wind River Canyon, Shoshone National Forest, and then up a monster climb (
http://www.routeslip.com/routes/14015) from the east gate up to the top of the caldera. West Yellowstone is just outside of the park's west gate, and has a couple of bike shops. We departed West Yellowstone towards Bozeman, MT - 20 miles of climbing and then 70 miles of decending following a river. Narrow, winding roads on the road to Bozeman though.
Regardless, its a beautiful and enjoyable part of the US to tour through. Recommend Glacier as well, and make sure you bring mosquito/fly netting if you elect to head that way.