For fine dining in Grand Cayman, my favorites are:
High end: Pappagallo Ristorante, The Great House, and The Wharf. There are all sorts of options at the resorts as well. Now that the Ritz Carlton has opened, the bar will be raised considerably. I'm told that they have 4 or 5 restaruants, all of which are highly thought of.
More relaxed, but still excellent dining: The Lighthouse, Calypso Grill, Copper Falls Steakhouse, Decker's, Bamboo (for Sushi), Reef Grill (for fish).
For the lunch thing, or casual dining, I like: Cafe Medeiterraneo, Cassanova's, and Ragazzi (for Italian), Canton (for Chinese), A Taste of India, The Lobster Pot, Thai Orchid.
For the 'local' thing, cheap, totally casual, and a true taste of Cayman: Champion House II, Cracked Conch By the Sea (cheapest Sunday brunch), Liberty's, and many others that I would take you to, but only after giving my "full and fair disclosure"
For a 'pub crawl' or to catch some sports (but still safe food): Lone Star, Durty Reid's, Fidel Murphy's Irish Pub.
Out of the way places that are worth it when you have time to wander: Rum Point Restuarant and Kaibo Yacht Club.
If I had to pick just one (i.e., if my special lady was taking me out for my birthday), it would be Pappagallo.