I have gone up the east coast, hugging the coast, twice from Florida to New York. There is a ferry between NYC and Atlantic Highlands. You can take US9 down to Cape May. This is a good bicycling road with plenty of shoulder and facilities. The only drawback is a 2 1/2 mile stretch over the Mullica River near New Gretna where you have to ride the shoulder of the Garden State Parkway. Both times I did it, hammering hard, I was passed by cops but they ignored me.
The huge ferry will take you from Cape May to Lewes DL. In Ocean City MD ride down the boardwalk. A bit crowded but right pleasant. When you get to the Chesapeake Bay Bridge just go to the toll offices and ask for a ride across. They will grumble a bit if you don't call ahead but you'll get the free ride with a maintenance man.
In the Outer Banks of NC you will take a bunch of delightful free ferries.
There is a campground right in Ocracoke. Avoid the crummy, overpriced motels in Morehead City. Go to the very nice Forestry Service campground at Cedar Point instead.
In South Carolina avoid 17 and alt17 south of Summerville/Charleston. I've ridden both and they are as bad as it gets - narrow, two lane, shoulderless and very heavily trafficked. You might want to cut inland here. Get back on 17 where it parallels I95 and take it all the way to Florida. Just north of Jacksonville at Yulee cut over the coast and head south. Picking your way through coastal Jacksonville is a bit trying (Take the Mayport ferry) but don't even think about cutting west on A1A just below the FL-GA line. It is absolutely no place for a bicycle.
Then enjoy the Florida east coast. You won't be bored for a minute. I love it.