We go down there every year to do art shows and 2014 will be our 6th year (time flies).
You don't say if you want beach or inland. As someone else suggested, try moving around a bit to see what you like. We almost exlusively do the state parks because we like to walk trails, etc. and because they are nicer (IMHO)...they don't squeeze you in like a parking lot. Some privacy and a natural environment.
Being more specific as to your preferences would be helpful. Me? I would just pick a handful of state parks and see what is left at this point...the more north you go will have openings and make a schedule and see many parts of Florida.
You can pm me if you want specifics or just ask on board.
Donna
