I agree about Horseshoe Bay. It is a beautiful beach. (Though Cinnamon Bay on St. John is way up there too.) One of my favorite things to do is visiting Gibbs Hill Lighthouse.🙂 Then there is Ft. Hamilton, riding the water taxis, Crystal Cave, Elbow Beach, wandering around the Dockyard, visiting St. George.
We found plenty to do during the 3.5 days that we were docked there. Never felt there was lack of something to do or explore and also didn't feel rushed, or time constrained, like we sometimes were in the Caribbean.
Bermuda is also a very safe upscale place where you don't have to spend much time watching your back. Certainly no one is going to be asking if you want to buy drugs.
Bermuda is also quite expensive. Don't go with plans for bargain shopping. It isn't St. Maarten or St. Thomas.