Grand Cayman for a week
The big hotels have some good restaurants, but are more formal and pricier. Had a great meal at 7 at the Ritz, but it was expensive.
For less formal with teenagers - Coconut Joe's, Hammerheads, and Rackhams. Hammerheads and Rackhams are almost right next to each other and have outdoor seating with nice water views.
If you have a rental car, make sure to go to Rum Point for lunch (at least) one day. Very nice and relaxing beach area with chaise lounges and hammocks scattered around that has tasty food and a beach bar.
Pappagallo has a nice location and makes their own pasta, but you will need a car or taxi to get to them.