I'd also recommend Bluewater. We have always stayed on the Bay. The Tiki's we had, had Isinglass roll down sides for the wind. But we didn't find the wind too bad. Bluewater is 14 miles from Key West.
Another choice is Boyds which is as close to Key West as you'll get. Sites are much smaller and crowed. It's also in a so-so area. But it's very close to downtown. It'll be less expensive then Bluewater.
We have friends that have stayed at a small campground on Geiger Key, which is also very close. We have eaten at the restaurant there and it's very good.