Michelle and I travelled from Missouri down to the gulf. Went as far east as Pensacola, Florida, then headed west along the coast. Perfect for a bike, but you have to plan on rain showers off and on.
We camped nearly the entire way, but we enjoy camping. The state parks all had showers, etc., so it was nearly like home for hillbillies like us!
We went in late June, which is the start of hurricane season, and it was as hot as hell. But it was well worth it. You'll have a blast no matter how you go!