I have a Florida holiday planned in early April and we are specifically staying on the Keys at Key West, so that I can bird Fort Zachary Taylor each morning, as its a real hotspot for passerines moving North and especially Warblers:
Its a 10 minute walk/short cycle ride from many hotels/guest houses. I also intend to take a trip to Dry Tortugas, whilst staying on Key West and by boat or sea plane:
Apparently its a bucket list spot for N.A Birders. Note you can get an internal flight to Key West from several other main Florida Airports.
For my second week away, I'm staying on Anna Maria Island further up the west coast and this has a great spot, which is again good for migrating passerines, by way of Leffis Key:
I've stayed here before and seen some great birds, such as Yellow-billed Cuckoo and Ovenbird, plus many other Warblers. Friendly local birders too! Also a free bus, which travels up and down the island all day long.
In general, one does need a car to get the best out of Florida.