You won't find much there. You may be better of driving to Marathon 18 miles north. There you will find the 2 places I go each time:
ANNETTE'S LOBSTER & STEAK HOUSE - Dinner
MM 48 3660 Overseas Highway
Marathon , FL 33050
The Cracked Conch Cafe - Lunch - GREAT conch salad
4999 US Highway 1
Marathon, FL 33050
I live in Marathon, and agree that there are a number of great outside places here. Locals love Burdines and Castaways (considered by many to be the best restaurant in the area). Also good are Dockside, Keys Fisheries and Frosty's. The Stuffed Pig is a popular breakfast diner. Great Thai food in the building next to Annette's (which someone else already recommended to you). I heartily agree with the recommendation you received for No Name Pub. The Island, Sparky's and Cabana Breezes are also highly recommended.
Enjoy your visit!
Another Marathon Chowhounder here...In Marathon I can only reccomend Franks Grill (a locals place) and Butterfly Cafe (an upscale tourist place).
The Meteor, in Key West, used to be great but new owners (in the past year or so) don't quite have the same recipes somehow and really raised prices.
Boondocks is always more than acceptable as is the Hogfish Bar and Grill on Stock Island.