Florida State Parks, none in Key West proper.
Bahia Honda State Park at Big Pine Key is some 37 miles from Key West
Long Key State Park is at mile marker 67 (from Key West).
There is a KOA a little further up, mile maker 70.
I've stayed at these three. They are clean. The KOA can resemble a parking lot at times. I prefer the State Parks but they dont have a full hook up, just water and electric. The dump station is on the way out of the park.
I have not stayed at these, but the seem okay:
John Pennekamp State Park is a mile marker 102 (far from Key West), in Key Largo.
Sugar Loaf KOA mile marker 20 (20 minutes from Key West).
We looked at Knights Key in Marathon mile marker 47 the bathrooms were old and filthy (about 3 years ago). If you talk to them ask if they have remodeled.
http://www.keysdirectory.com/knightskeycampground/
Here's a link for some more:
http://www.rv-clubs.us/florida_rv_ca...html#Southeast
Can't comment on any of these, but you want to make sure and ask about how much space in between sites.
Enjoy the keys try to go while its cold. In case you are not from Florida, if there's no breeze, the mosquitos will eat you alive.