Mountain loop trail around Cloud Peak, mostly within the designated Cloud Peak Wilderness area west of Buffalo, WY. Elevation ranges from 8,300 feet to 10,925 feet, climbing over 4 passes. Much of the route is above timberline for beautiful views, and passes by 4 lakes. There are 4 main access trailheads, so hikers can connect from the east, north, west, or south - each adds a few miles of hiking before starting the loop.
The route is only the trail #038, from where the hiker set foot on that trail, to completing the loop back to the same spot, so be sure to check you time when you start and finish the loop.
https://www.alltrails.com/explore/trail/us/wyoming/solitude-trail-038 has a map, entering from the north.