There are many places to hike in the Bighorn Mountains. One of my favorites is the hikeup to Misty Moon Lake. To reach the lake travel to Tensleep and then up Tensleep Canyon to the top. You will come to a dirt road that has the trailhead a ways down it. The hike is about 6 miles up to the lake and is relatively low in its vertical gain. There is camping at a lake about 1 mile before Misty Moon that is spectacular. From either locations you can travel up to Bomber mountain and check out the plane wreckage or travel further to Cloud Peak, the highest peak in the range. Us the USGS 7.5 Lake Helen Map.
