I have a couple of personal favorites. For a romantic, quiet dinner, try Cocoplum Gardens located on the road to the airstrip. Its kinda a walk, but they will pay your one-way cab fare if you use Jasmine Rentals. Another nice thing is that you are not right in town, no disturbing golf carts whizzing right by and the food is impecable.
Caye Caulker has lots of choices for restaurants, I also like Jolly Roger's, Rasta Pasta, Happy Lobster, Vespucci's Table, Cindy's Cafe for breakfast (best coffee on the island, homemade yoghurt and bread. The Rainbow Restaurant has a wonderful deck over the water. Dave's BBQ on Middle Street is good also.
I'm sure I've left a few places off, but you'll see when you get here that the choices are many.