Looking for a honeymoon spot with good eats

[FoodieT]

My fiance and I are planning a honeymoon for the first week of April. I'd love to go somewhere warm (without being stifling and humid) and beach-y and private... but not so private that my only food option is the resort or two beach shacks. I'd like a plethora of dining options, both hidden holes-in-the-wall with local grub as well as a few stellar fine dining spots.

We're open to pretty much anything. I'm pretty adventurous when it comes to eating things, so sign me up! Good seafood would be awesome. Any suggestions on a location as well as a few suggestions on where to eat there?