Knowles Beach is a hidden get; From the Governors Airport, go about 3 miles south toward Governor's Harbour; take a left at the hideous orange poles, which says "Breezaway Estate"; go to end.
There are a couple of rental houses on the beach, but you will, most likely, have it to yourself. You can hike about 10 miles going north, and it's a great place to jog.
As you can see from this nautical chart, there are many close reefs for good snorkelling.