FL has a variety of beaches. Greater Daytona Beach area (which is Volusia County, Ormond Beach to New Smyrna Beach) has riding on the beach and at low tide, your road bike will be able to ride on the sand, otherwise a beach cruiser is something you can ride. There are the Keys/Key West, FL. Also Fernandina Beach, Jacksonville, to Flagler Beach (County). Also there are beaches all up and down the East coast of FL, whether you want to actually ride on the sand or not, I've never tried. I live in Miami, road biking can't be done on that sand as is most of South FL, so that's asphalt riding within view of the ocean in between the condos. Trail riding ? Miami has it in some of the county parks, but they charge a fee and it's a couple of dollars.
I would also think the Carolinas and Georgia have beach towns. Gonna be hot in the summer though. Savannah, GA., Cape Hatteras, NC and so on.