Start off on a steep doubletrack climb up the front of the resort. There are singletrack loops branching off as you go up. If you continue all the way to the top, follow the signs to the, I believe it was the Wilson Canyon loop. That was the section of the trail that I rode, but there are many different single track loop options out there. According to a map in a bike shop in town, Wilson Canyon was the most technically challenging ride, rated an "expert." It was no big deal, but it was a decent downhill. Nothing world class, but it is right in Jackson.
So when you get down to the highway, cross it, hang a right on the bike path and take that back to Jackson.
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.singletracks.com/item.php?c=1&i=2766