Jackson Hole, Grand Teton National Park, Yellowstone National Park, Palisades Reservoir, 4 wheeling in the mountains
Basically it's all about the outdoors there. It's either driving to see the sights or camping, hunting, fishing, 4-wheeling, etc.
In Star Valley itself you could probably rent side by sides and go up in the mountains, but there aren't a lot of "things to do."