Recently back and thought I'd share:
Breakfasts: Doreens (3 times) everything is amazing don't miss (cannoli and crunchy french toast, omelettes, crab eggs benny; Petit Soleil (2 times) because the waffles are the best, lightest and fluffiest we've ever had and NeNes which is standard diner breakfast fare
Lunch: Empire Bagel, Quinns takeout (surprisingly good and way better than the Marriott beach service menu)
Dinner: Cocomos (fun, great vibe, food is okay, you can get in and out with dessert in an hour which is handy with kids) The Little Bar (stone crabs are a must, and the kids hot dog was terrific), DaVinci (love the location and eating outside by the fountain, food, service and wine were great, esp the lasagna), Fin (hands down our best dinner spot on the island, do not miss an opportunity to eat there, I think its closed Sun and Mon; seriously it is amazing food and gracious service; we didnt bring kids, but if you went early, you could), Dolphin Tiki (beautiful spot, food is fair, so better for drinks and maybe a salad, than anything else; whatever you do don't get the pulled pork), Cafe de Marco (delicious, we're are quite partial to Old Marco, which is very charming as is dining outside there; don't expect a quick meal, owner really cares about your experience)
Additionally Bebe the ice cream place in the Marco Walk by DaVinci is amazing for ice cream, great flavors; the new gelato place in the Old Marco shops is little known, but absolutely delicious as well. Latter closes at 9pm (opens at 1pm after daily delivery form sister shop in Naples) Happy eating!