The best park in the Keys, IMHO is Bahia Honda State Park. The park is located on Bahia Honda Key, a beautiful island on the south end of the 7-Mile Bridge connecting to Marathon Key. Bahia Honda SP has a small campground with a number of the sites right on the beach located in the bay at the south end of the key. We have stayed there with our 20 ft Flying Cloud. Some of the sites are tight, but the park is terrific. There is swimming in the protected bay, as well as along a couple of miles of beach on the east side of the the key. Marathon key is the next key to the north and has shopping, restaurants and other attractions. Key West is about 2 hours to the south, close enough for a day trip.
Check out the Florida State Parks at Welcome to Florida State Parks
. You can register online through the Florida park website using ReserveAmerica. It is essential to sign up as soon as you are permitted to make your reservations (I think it's about 11 months in advance) since all of the Keys camping gets filled up well in advance.
Good Luck with your Florida vacation. It's good that you're planning ahead. If I can help with any specific questions, let me know.