VISIT: Wyoming's 31 Named Islands
As you might imagine most of these islands are on the Western side of the state, in Teton and Sweatwater counties. Most are in rivers, just a few are in lakes. I was able to find camping near these islands in such places as the Island Park Campground. But I was not able to find camping on any island. That does not mean that it can't be done. Some of the most notable island are: Jackson Lake - Out of the 31 islands in Wyoming, Jackson Lake boasts of 1/3 of them. Some of the islands at Jackson Lake are: Arizona Island, Dollar Island and Elk Island.
Source: kgab.com