Shuckum's and Dusty's on the West end, two different places. Dusty's food isn't very good except for their oysters, and they have two world champion oyster shuckers that work there.

Captains Table in town is excellent, all of their seafood is local and fresh including their oysters. Rustlers Reef is also good, which is in town.

I'm sure there are more in town, I can't think of any more at the moment though.

Shuckum's is the only place that has an outdoor area, but all of those places have great oysters.