Hello Carsten,
I haven't really used a camper down here and can only comment on what I've seen. You might get away in a shopping mall parking lot or you might get rousted by the police in the middle of the night. I imagine enforcement varies, there really are a lot of campgrounds. There will be some demand as you will be traveling during spring break and the campgrounds are also popular with the college kids. Others have input on this in SE Florida?
The websites for both public and private camp grounds appear in the link I posted about this at:
http://fksa.org/showthread.php?t=2278 (there are other posts in that section that may be helpful to visiting kiters,
http://fksa.org/forumdisplay.php?f=89).