We are not fans of NCL but love Bermuda. My advice would be to cancel and book Celebrity or HAL out of Boston. In fact, we were in Bermuda once and people saw our towels from HAL and said they wished they were on our ship. They were on NCL and hated it. Other people from their ship chimed in in agreement. We had already been disappointed with NCL and totally understood.
You don't need to do ship excursions in Bermuda. You can buy a transportation pass for about $30 that includes unlimited buses and ferry for 3 days. OR you can buy what they call a book which is 20 tickets for one ride each on the buses. A family can share them and they run about $15.
If you like to snorkel, Church Bay and Tobacco Bay are the best spots. Church can often be rough in the afternoon so go mornings. The most popular beach is Horseshoe. If you have small kids, Jobson's Cove is very calm and you can walk, not along the beach, but through the land, to Horseshoe. Then pay the $2 for the shuttle back up. It is a very steep walk in the heat.
You will be docked at the Dockyard and there is a beach there. We have not been there for years and I have not heard good things lately. I am sure with all the big ships docked out there it gets pretty crowded.
Go downtown on I think Wednesday for Hamilton Harbor Nights. It is fun.
St. Georges is very cute to walk around. It is near Shelley Bay, St. Catherine's Beach, and Tobacco Bay. If you have the transportation pass, take the express ferry.
There is an aquarium and cave that are popular.
Go to cruisecritic.com the ports and read about Bermuda.
It is beautiful!