No, you are fine.
There will be spaces in central Florida, and probably north Florida and the panhandle as well. We stayed a few days in a CG north of the Villages, next to a Camping World. It had space on short notice. They were roomy enough but nothing special for the non-seasonal campers. I can't remember the town.
I would also see if I could get a week at the Jetty Park in St. Augustinexxxxx, er, Cape Canaveral.
http://www.jettyparkbeachandcampground.com/You could also look into Gulf Shores, AL. And Texas, although you can't count on temps above 65 for a given month.
Personally, even though we go to AZ, I would not advise it for only a month. It's a cold long journey to get there and back when you only have a month to play with. You'll spend 8 to 10 days traveling, and freezing. One time the trip out was so cold, we stayed in hotels all the way till we got to Las Cruces. Under 20 degrees the whole way, through Amarillo. That was the northern route through OK, but the one day longer southern route was not any better. In the middle of winter, for planning purposes, from IL to AZ you have to assume you will be dropping south at least as far as Texarkana, then across through Dallas to El Paso. One year we had to go farther south and cross TX down through Waco, Junction, etc. And always keep an eye on the weather en route, for snow and ice storms. Be prepared to head farther south.
All that said, in early Jan we are headed to AZ!
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Currently RV-less but not done yet.
