Try Grand Teton National Park just south of Yellowstone. Flagg Ranch between the two parks is a nice place to stay. There is Old Faithful Inn and others. Cody is also a nice place to visit east of Yellowstone with the Shoshone National Forest and the Bridger Teton National Forest near Big Piney. The Big Horns are nice near Sheridan and the Wind River Range near Lander and the Snowy River Range in the south central part of Wyoming.
I suggest Yellowstone National Park which is in the northwest part of Wyoming. Very beautiful place full of geological oddities that you won t see anywhere else in the world. here is a link to the tourism department. http://www.wyomingtourism.org/