There are loads of good beach towns in Florida, but I'm not sure I can say there's one that's better than all the rest. Key West, Clearwater, Palm Beach, Miami Beach, Ft. Lauderdale, Hollywood, Naples, Cocoa Beach, and on and on...
Name one YOU like, and say why you like to ride your bike there. Are there good bike facilities - lanes, MUPs, good places to park and lock? Bike friendly businesses and attractions? Bike sharing, or other rentals?
Pensacola Beach. The good: dedicated bike lane for the first 3 miles on the east side of the bridge...then opens up for miles with very little traffic and great scenery all the way to Navarre Beach. There is most always a strong tailwind when heading east (think 30mph+ with a little effort on the pedals). The Bad: Can get super hot and humid in the summer. The traffic can get pretty apathetic to cyclists at peak hours during the day. Almost always a strong headwind when traveling west.
Hollywood Beach has the Broadwalk - a 3+ mile long paved beach walkway bordered by sand on one side and shops, cafes, motels, and parks on the other. The good: no cars, and the walkway has a dedicated bike lane, lots of scantily clad beachgoers, plenty of places to stop and get a bite to eat. The bad: heavy pedestrian traffic during the season limits speed to the mellow cruising range in some areas.
Much of A1A (the beach road along the east coast) in Florida is great for cycling. The counties serviced by the Tri-Rail are great if you want to cover some distance in one direction, then ride over to the train for a quick & cheap ride back.
Ponce Inlet, South of Daytona Beach/part of the Daytona Shores area.
Morning traffic is non existent. There's really only 2 roads that fully run North/South though. I did some running there before I started riding, and there's at least one very large group ride there on the weekends. Between the beach, the park, and the lighthouse, it's a pretty great area.
After you're done on the road, you can relax on the beach then take a cruiser or mtb for a ride in the evening on the beach.
All that said, I'm curious about the Amelia Island area. I haven't been there in years and wouldn't mind taking a vacation (and bringing the bike).
Edisto Beach has a paved trail most of the length of the island and bike lanes on more of the streets. Bike racks at beach access points. SC 174 has a bike lane out to Palmetto Road giving some more paved miles. Palmetto Road is very pleasant. On hybrid tires the state park has a nice dirt trail as well. SC 174 inland of Palmetto Rd is not friendly for bikes except maybe off season. It is narrow, no shoulder and traffic is fast. There has been talk about adding bike lanes out to the intercoastal bridge, but I have seen no progress toward that.
I probably ride 20 to 25 miles a day when I am there. I'm a birder, so the bike is nice to take me to various habitats in the area.