I have 3 absolute favorites in Bermuda, Elbow Beach, Horseshoe Bay and Tobacco Bay - all for different reasons. The one that would best suit your qualifications would be Elbow Beach. If you want to do some excellent snorkeling in shallow, calm protected waters - go to Tobacco Bay. Horsehoe Bay is the most picturesque. There are pictures and information about each on our sister site http://www.portreviews.com
. Here is the link to the Bermuda site: http://www.bermudaportreviews.com/index.htm
You will need to click on Hamilton and St. George's to find out about the beaches, as there are none I would recommend on King's Wharf.