The fort in Hamilton is full of history as is the Royal Naval Dockyard and St. Georges. Bermuda is an absolutely beautiful though expensive location. The transit pass is absolutely a must and allows you to take any bus or ferry on the islands. All of the houses are gorgeous and are pastel with white roofs. My girlfriend and I walked from a bus stop to Grape Bay, a private beach, which was gorgeous with a lot of tide pools that you wouldn't get a chance to see at the popular Horseshoe Bay or Elbow Beach. The best snorkeling we found was in Tobacco Bay within a short walk of St. Georges town center. There was as much wildlife as what I saw the last time I was in Cancun, though this could be seasonal. Also if you're there in the summer, make sure to check out harbor nights in Hamilton, it is a lot of fun.
The White Horse Tavern had wonderful fish and chips. Having been to England and Ireland these were definitely up to par. Make sure to check them out as well as the island delicacy of Conch, though I'm not sure if this was local. They were still amazing.
I had the best sushi I have ever tasted from Beluga Bar which is located in Washington mall in Hamilton. I highly recommend it. The chef offered us a few free pieces of local Wahoo Nigiri (amazing) and made us a roll that wasn't even found on the menu. The freshness and service was second to none.
Flannagans in Hamilton was a nice lunch spot and has quite good traditional pub food. The waitress here told us about the Grape Bay (the private beach we snuck on to). Make friends with the locals. They are awesome people and will do whatever they can to help you out and give you some great ideas.
Make sure to try a dark and stormy. Local dark rum and ginger beer are quite the combination. Once you leave Bermuda you can even ask for them on the ship. It is an absolute treat.