Joe: I like Little Hole, at the dam you park your car up high and then after fishing have to climb the staircase to the parking lot.
Check out this hatch chart: Hatch Chart
Looks like Terrestrials, Caddis and PMD's.
Also check out these fishing reports: Green River - Below Flaming Gorge | Utah Fly Fishing Reports & Conditions
Green River Fly Fisher - Fly Fishing Report for July 29th, 2012
Green River Report - WR FLY FISHER