We were there about 4 or 5 years ago and really enjoyed it with the kids (7 and 9 at the time). We took the bus (which is very inexpensive) rather than the ship-planned excursions. We went to the Bermuda Aquaium and Zoo http://www.bamz.org/ which was beautiful.
We took a 15 minute walk to Tobacca Bay. It is small and enclosed by rocks so that there are no waves so the water is perfect for kids of any age. W snorkled there all day (you can rent equipment there or bring your own) The water was warm and the marine life was plentiful. That's actually where our kids learned to swim, paddling around with their snorkles. Here are someone's pics I found online just now http://www.metrocast.net/~hiker/photo106.html
One evening we took a horse drawn carriage ride around town. It was a great way to see the city.
We also went on a snorkling trip to see some of the shipwrecks. It had been raining all day so the visibility wasn't great. I much preferred the snorkling at tobacco bay.