We went on a fabulous cruise to Bermuda in 2000. We stayed at King's Wharf too. One day we took the bus to Horseshoe Bay beach... this is the most beautiful beach I think I have ever been too. You can snorkel there too. You can go for a long walk or just sit or swim... THey have facilities and chairs to rent. The water is warm and clean and just lovely... The bus goes right by there.
As for sightseeing, one day we just got off the ship and spoke to one of the cab drivers at the pier. He was a great guy... We arranged a price, piled in, and he took us all over the island, explaining things as we went, and allowing us time to get out wherever we wanted, for as long as we wanted. I would recommend this! We had a great day and saw many of the highlights of the island. It was very reasonably priced as I recall, plus we added a nice tip for the wonderful driver.
Have a great time... Bermuda is wonderful!! You're gonna love it!
PS - we did book one excursion at the time, it was to a nightclub to hear a steel drum band. While the music was nice, the overall excursion was overpriced and most of our group was unhappy with it.