We just came back from Grand Cayman this Saturday and stayed at the Marriott. Don't bother with the food there, the prices are almost comical.
For Breakfast we ate at Eats Cafe. The same owner runs Legendz and Yoshi Sushi and the place is spotless. Blueberry Pancakes are 3.95ci and you can get a normal breakfast for under 10bucks US.
We had several recommendations for a sushi place called Bahamas, but we didn't like it. Not sure if it was just a bad night in the kitchen or what, but the sushi was mediocre at best.
There is also a brand new place north of 7 mile beach called TimBukToo. They just opened, it's small but the food is good and my wife and I ate breakfast there twice. It's right after the traffic light heading up to DiveTech/Turtle Reef.
We also ate at Coconut Joes (food was good), Hammerheads, Tiki Beach and Guppies. We also skipped lunch a couple of time, eating a decent breakfast and a later afternooon meal, skipping the late night dinner. That was a big cost savings and we munched inbetween.
Breezes in Georgetown has a good 9.99 menu if you have ecclectic tastes, like Curried Goat and Oxtail. The latter was excellent. There was a steakshop that advertised a 14.99 sirlion but when you get to the restaurant, they don't mention it on the menu. We inquired and sure enough, it existed and we ate for about 40bucks with drinks.