Cemetary beach is lovely and quiet and more than 5-10 minutes from town, particularly during rush hour (allow yourself 30 minutes back to town if it's after 4, just to be sure) It's the north end of 7 mile beach, and where they shoot a lot of the posters.
I wish I were there now!!!!! Just talking about it is making me wistful...
Great snorkling. Nice shade trees in addition to the sun and sand. No facilities. For the quiet and pristine beauty , you are trading off the jet skis and parasailing and touristy types of things, so it depends on what you want. Between Georgetown and cemetary, there are a number of hotels, beach bars with facilities and a public beach with facilities that provide a variety of amenities.
Just keep your eye out for what strikes your fancy. Your cab will pick you up at a pre-arranged time at Cemetary, if you like... or if you're near a beach hotel, you can always catch a cab there.
Have fun.