What kind of food do you like? Seafood? Pizza? Mexican? Steak? Burgers? Italian? There are places nearby that cater to all of those.
The restaurant at Humphrey's Half Moon Inn is quite good for lunch or dinner - it's mostly seafood. The Brigantine, on Shelter Island Drive, is umm...steak and seafood, I think? Miguel's Cocina, on Shelter Island at Scott St. serves pretty good Mexican food. If you like burgers, The Boll Weevil, on Shelter Island Drive, serves not fancy, but good burgers and fries.
For breakfast...hmmm. There's a place called the Point Break Cafe that's in a little strip mall on Scott Street, about a block off of Shelter Island Drive, that serves a very good breakfast (they serve breakfast all day). There's also a Denny's a few blocks away. Marvelous Muffins has muffins and other pastries, and that's pretty good. It's also on Shelter Island Drive, across from Miguel's.
Old Venice is a nice Italian place on Scott Street, about three blocks from Shelter Island Drive.
Umi Sushi, also on Shelter Island Drive, is very good - I don't really like sushi, but they have good teriyaki and tempura, also.
Oh, and if you want a REALLY nice (but pricey) dinner, try Roseville. That's on Rosecrans St, a mile or so from the Best Western.