If you are looking for a guide, try Four Seasons Fly Fishers out of Heber, they fish most of the areas waters. Lots of water is open all year long within 1 hr of Park City because of all of the dams.
Provo and Weber are good bets, check some websites for the Weber River, it holds lots of large fish and has good access along the roads
Better yet, stay at Johnson Mill b&B in Midway UT and fish the pond or the stream running through the land
Good Luck
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