The East Entrance of Yellowstone National Park is about 52 miles from downtown Cody. This route takes you along the Buffalo Bill Scenic Byway (U.S. Hwy 14/16/20), a beautiful drive through the Shoshone National Forest and the Wapiti Valley before reaching the park. The next closest entrance after that is the Northeast Entrance near Cooke City, MT - but that's a much longer drive from Cody (about 3 hours)