Sometime in June? You must not like the man very much! June in South Florida is muy caliente!
Anyway, there are a lot of great parks within 100 miles. The previous advice about the state parks was dead on. Florida has one of the best state park systems in the country. The vast majority of the campgrounds have water and electric and the newer ones have sewer. Jonathan Dickinson is great, as are all four in the keys: John Pennekamp, Long Key, Curry Hammock, and Bahia Honda. Long Key has been closed for renovation, but should re-open by June and that one is our favorite because you are on the beach. Tell him to stay away from Collier Seminole in Naples, though. There's not much to do there and the mosquitoes will suck you dry. The same goes for Everglades NP. I wouldn't go there outside of January or February.
There are also some very nice county parks. In Miami-Dade, Larry and Penny Thompson Park is very nice and it is adjacent to the Miami Zoo. Broward has Markham, C.B. Smith, Easterlin, and T.Y. parks which are all great. And Palm Beach has John Prince Park as well as the South Bay RV Park.
The key to successful South Florida camping in June is to be as close to the water as possible. Anywhere in the Keys is fine. There are lots of private CGs down there in addition to the SPs mentioned above. I've camped at John Prince in the summer and I'd go to Dickinson, but I'd stay at the Pine Grove campground where there's always a seabreeze.
Drew & Kendra
Lucky & Bentley the camping dogs
2011 Ford F-150 SuperCrew EcoBoost w/tow pkg.
2012 Rockwood Roo 23SS