The town of St. George is probably my favorite place in Bermuda. It perhaps is a bit too laid back for me to want to live there, but it's just about right as a place to visit.
It's located on the south side of the thickest part of St. George's Island on the north side of St. George's Harbor. As mentioned on the main St. George's page, this town was the original settlement in Bermuda, and also the original capital.
There's a fair amount to do in St. George, even though it's small relative to Hamilton. There's quite a bit of shopping and dining. Here are some places I think are worth visiting...
The Bridge House:
Built in 1650 as someone's residence, today it's the location(and home?) of Jill Amos Raine. She is one of the local artists. Most of her work is watercolor(which Bermuda is perfect for), although she dabbles in other things.
The Carriage House:
This is my favorite restaurant in Bermuda. Granted, I haven't been to them all, but still... It also happens to be the most expensive restaurant in St. George. Believe me though, it's worth it. If you're visiting St. George, you have to eat here.
The White Horse Tavern:
Located on the Square, it's got a great outdoor eating area right on the water. It probably has the second best food in St. George's. Located inside are a bar, and also a game room upstairs.
You've got to have ice-cream, right? Not to mention they're the only place in St. George that seems to have this awesome chocolate mousse cake.
Not what you would expect on a list of where to go, as it's a drug store, but... If you need it, they have it here. (Including the Boston Globe, but not before 4:00pm!)
St. Peters Church:
Built in 1620, this is the oldest Anglican church in the Western Hemisphere. Surrounding the church is a graveyard where some of Bermuda's most important people are buried. The inside is also impressive, being completely worked in Bermuda cedar. Somewhere along the way, they decided to build a new church(possibly even a cathedral?) in town, but abandoned the project partway through. You can visit the "ruins" of the the "new" church, which is pretty old itself!
Other places of interest: Ordinance Island(home of the Deliverance replica), Featherbed Alley Printery, Town Hall, and although it's not exactly in town, the Bermuda Biological Station.