It's been a few years, but some of our favorite restaurants there are in St. Georges. (You'll stop there as well as Hamilton and the Royal Naval Dockyard) Athena will have to confirm if they are still open, but our favorite is Blackbeard's Hideaway. It's just up the road from St. Catherine's beach. No place better to watch the sunset with a Dark & Stormy! The food is wonderful there. We pretty much ate our way through the menu last visit there and loved everything. Mostly seafood prepared expertly. By the way, some of the best snorkeling around the island is from the tiny beach at the bottom of the steps from Blackbeard's.
At the Dockyard, try Freeport. It's more of a "locals" place. The decor isn't as fancy as the pub in the main Dockyard building, but the fish & chips are delicious, as are the fish cakes and the Bermuda fish chowder, which you shouldn't leave Bermuda without tasting. Be sure to add the sherry pepper sauce and rum to your chowder.
While on the island be sure to visit the BAMZ---Bermuda Aquarium, Museum & Zoo. The aquarium is world class and the zoo part has some interesting animals.