There are miles and miles of trails on Snow King Resort right in the town of Jackson to hike. Some of the trails are very steep, and some aren't. The views off of the top are definitely worth the effort, though!
The resort looms above Jackson, all you have to do is go down to the end of Cache Dr. Park at the ski resort parking lot at the bottom of the lift.
http://www.tripleblaze.com/trail.php?c=3&i=2362