You can play golf, snorkel, jet ski, para-sail, go horse back riding, or go on a glass bottom boat ride to see coral and fish. There are a couple of attractions near St George called Fantasy Cave and Crystal Cave, if you like that type thing. You wouldn't think that in Bermuda where you are very few feet above sea level there would be caves, they do have water in them.
The main things to do in Bermuda is enjoy the beaches as there are lots of them and they are beautiful.
The town of Hamilton is the largest on the island and its kinda interesting. It has a few stores, a grocery store, a museum, an old church and a few restaurants and bars. The Kings Dockyard is on the opposite end of the island from St George and it has a small shopping mall, a museum, and a new water attraction/beach called Snorkel Park at the Dockyard
Here are some web sites for you on Bermuda activities:
http://www.bermuda.com/beacheswatersport...
http://www.bermudatourism.com/index.aspx