>>I am planning a one week bike ride with my 13 year old son in March>>
It may be a bit late for you, but cycling along the Atlantic coast can be quite nice. ACA has a map that covers the stretch from Jacksonville south to Ormond Beach. One can follow the coast road (A1A) all the way to Fort Lauderdale before encountering any serious urban sprawl. Traffic is there, of course, but auto drivers seem conditioned to expect cyclists and the coastal roads generally have modest speed limits.
Highlights could include the St. Augustine historic district and fort, wandering around Merritt Island NWR and the NASA complex, watching the surfers at Sebastian Inlet, camping at Jonathan Dickinson state park and lounging around Jupiter Inlet, and cycling along "millionaire's mile" in Hillsboro Beach.