South of I-4 along US27 you will find some possibilities.  2 years ago we didn't leave Michigan until February 1st, without reservations other than one place down in the Keys and we stayed at 8 different campgrounds from north to south.  Depending upon any amenities you might be looking for, there will be parks for you.  
Sebring is a nice area.  We stayed at a place called Whispering Pines there for a couple of days.  They had plenty of sites available for a very reasonable price.  Sites were a little tight, but the residents were nice as were the managers.  Below is a clicky for Sebring at RV Park Reviews.com.  This will list the park I've noted above as well as others in that area with camper ratings and comments.  
http://www.rvparkreviews.com/regions/florida/sebringAnother park we stayed at for a few days was in Winter Haven, Cypress Campground & RV Park.  We wanted to stay in that area to attend a Detroit Tiger spring game in Lakeland.  See the clicky for the Winter Haven area.
http://www.rvparkreviews.com/regions/florida/winter-havenBoth these places had pools, activities, and were fairly priced.  As I said, we stayed only a few days in each location because we were trying to visit several parks for a few days each to see the area as well as the parks themselves.  Not sure what they are like for the long term.