I absolutely love living in Riverton, WY for its untouched nature, rich history, and the fact that Yellowstone is only a short drive away from home. The town offers a giant National Forest that is never short of a beautiful and explorative hike, there are hot springs nearby that are amazing to relax in, and if you're lucky you'll catch a scene full of bison that roam the land.
The museums in the area are rich with local knowledge of the local native peoples and those who emmigrated from the Eastern shores and colonized the town. The only negative of this is once you've gone through the museums and seen them you've seen them. It's not something you can find something new every day at. There are special events in town honoring historic days and national holidays are observed. The community is lively and enjoys a good small town festival now and again.
There are some well directed plays at the Robert A Peck Art Center, and I don't know too many smaller town offering such honorable theatre. Another favorite place in town, if you like camping and sleeping at a historical monument, is the 1838 Rendezvous camp; a special place in which mountain men from the early 1800s met before returning to their lives in the mountains. You'll have to come by and check it out!