Look into the State or County Parks - I have never really had any problem there. RV parks / resorts may not be as accepting.
The State parks are less expensive. I have stayed at several in Florida over the last few months - and really like them.
County parks are great, too. Sometimes they are even better- but every county is a little different.
You can reserve or browse state parks through ReserveAmerica.com - but I recommend going to the park in person (they seem pretty booked in the winter time around Florida).
We just like Manatee Springs State Park - really pretty there