There are literally hundreds of miles of trails all throughout the back woods in Brian Head, which can be hiked, biked, driven, or snowmobiled on. Getting lost is an option here.
But to keep it easy, there is a trail through town that hikers can meander through, and the ski resort opens the lifts in the summer so that mountain bikers can risk their lives careening down the mountain. I hear that it's fun.
Georg's Ski Shop also runs a mountain biking business, where you can rent bikes, and, be driven to the best trails. Contact them at 14356772013.