There are nice campgrounds at Buckboard Marina (Private & Forest Service - the private has hookups) on the Wyoming side. In Utah there is a FS campground at the Lucerne Marina, just outside of Manila, Utah. Not sure if they have hook ups? All of these campground are fairly ugly being in sage brush country & very few trees. However, this is where some of the best fishing can be found on the reservoir. There is also the KAO in Manila, as mentioned above.
If you are looking for beautiful country, you need to get closer to the dam. There are several FS campgrounds - Fire Fighters Memorial (my favorite), Cedar Springs Marina & there may be others over by Dutch John. You are heading for a world class fishery, either on the reservoir or the river downstream of the dam. If you do not fish, try floating the Green River downstream of the dam in a rental raft - absolutely gorgeous.
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