Excursions off the ship in Bermuda are not necessary. This is one place that is very easily explored on your own.
Where to begin. In St Georges the town itself is a historic destination in and of itself. Shopping here is excellent and there are sevreal pubs to go to to try a locally brewed beer or ale or to have a Dark and Stormy (Rum and ginger beer).
Beaches to try would incude Tobacco Bay or St Catherines . Both have facilities, Tobacco Bay will be busier. Just 100 yards on the other side of Ft St Catherines is a smaller more private (but quite public) beach Achilles Bay. Use facilities at St Catherines Beach. There is a mini bus system that will take you from town to any of these locations. Round trip is $2.00 (maybe a bit more). There are several historic sites in town and a nice glass bottom boat trip can be taken from the harbor.
Take a bus to Hamilton for shopping , more historic sites. On the way there is Crystal Caves and a Glass blowing factory.
Other famous public beaches (all accessable by bus from Hamilton include Elbow Beach and Horseshoe Bay. There are many others.
Like snorkelling? Try Jessie James cruises out of Hamilton. Their 3 stop trip is one of the best I've done and the family running it are great folks.
From Hamilton take a ferry to Dockyards and spend a few hours in shops and galleries here as well . There is a Dolphin Encounter run out of this area as well.
Lots more on this great place to see and do. Suggest bermudatourism.com
as a source of information and Frommer's sells a good Bermuda guide book.