[gearhead]

A couple of things..
How old are you? If you can get the senior discount "America the Beatiful" card, get that ASAP. With it you can use US ARMY CORPS OF ENGINEERS (COE) campgrounds at half price, of an already cheap price. Also buy the book "CAMPING IN COE CAMPGROUNDS". It is indexed by states. I bought mine on Amazon. We just stayed in COE campgrounds near Agusta Georgia and Tuscaloosa Alabama, both great.
Just how warm do you want to be? Along I-20 can get some cool fronts. I assume a lot warmer than New York, but not exactly tropical. Warmest would be down along the coast along I-10. I would recommend southern Louisiana just for interesting culture and the great food.
If the weather along I-20 agrees with you you can camp in COE campgrounds next to the big lakes for about $15 a day which might be cheaper than staying home.