Although Utah is one of the top producers of gold in the United States, most of the gold comes as a byproduct of other mining operations for copper, lead, silver and zinc. Near Salt Lake City the greatest producer of minerals in the state is the Bingham Canyon Copper Mine. There are a few other successful larger commercial mining operations, so the total production in Utah is significant.
Recovery of placer gold was minimal and not enough to be of interest to the early miners, since it is extremely fine textured. Of greater significance were other minerals but the mining process is expensive and requires techniques such as cyanide leaching which is not feasible for a recreational prospector. But if you pan the creeks carefully you may see enough color to keep you happy.
Some of the placer workings that have been documented are:
Just below Flaming Gorge Reservoir in the northeastern part of the state, the Green River has been known to produce placer gold.
In the Abajo Mountains, check out Recapture and Johnson Creeks.
There are a few creeks in southeastern Utah that drain the Henry Mountains that are worth a look.
There is gold in the Colorado River, but it is tough to pan as it is extremely fine, and it takes careful handling.
In the Southwest take a look at the San Juan River for fine placer.
You may want to search for fine gold southwest of Salt Lake City in the Oquirrh Mountains, as there is fine gold in the creeks that run close to the Bingham Mine.