I've been to Bermuda four times, always on a cruise. It is, bar none, our favorite cruise destination because of how beautiful the island nation is.
First of all, cruise-wise, it is unique because it is the only trip one can make, that I know of, that you are there (on most seven-day cruises) three and one-half days. This is significant. If your ship goes there for a week, you will either be at one docking location, probably King's Warf on the western-most end of the island, for the whole time, if your ship is one of the larger ones; or your ship will call at Hamilton, the middle port for a portion and then move (weather permitting) to St. George on the east end.
Secondly, we have found Bermuda to be very safe and visitor-friendly. Most of the residents there enjoy a high standard of living, which trickles down to you having a very nice visit.
I don't know what the average age or physical situation is of the party you are travelling with, but for us, who are fairly agile and active, we always rent the scooters when we visit Bermuda. If you are careful, and drive the speed limit, tooling around the island can be exhilirating. There are no car rentals available to visitors: all cars driving past you are local people aware that you are a visitor and they take care and consideration passing you by.
I realize that one must be very prudent while scooter-touring the island, but the rewards are as seemingly infinite as the scenic wonders and amazing little beaches, parks, and post-card stops that there are to enjoy.
You can rent these scooters for your entire stay, parking them in the lots near the ship at night and hopping back on the next day. That said, be extra careful in the one big city of Hamilton; traffic can be heavy there.
If you wish to skip the scooters, certainly if you have children with you, you will find that the pink Bermuda busses can take you everywhere--all over this island. The people are so very friendly and will suggest many places for you to hop off of the bus to enjoy the various beaches and parks.
Use the shore excursion desk on your cruise ship to find out how to take part in diving or snorkeling trips, catamaran trips, golf outings--there are more courses per square mile than anywhere in the world, I hear.
There are easy-to-use ferries to take you from The Royal Naval Dockyard on the west end to the city of Hamilton, and to other parts of the island. I keep saying island---Bermuda is many, many islands....
What a wonderful place it is, indeed.