Less than a half mile walk from the resort, are the Versailles Gardens and French Cloister. It is a beautiful place to walk around and enjoy not only the flowers, statutes but it is right on the water.
The harbor side has a great selection of shops and restaurants and a fun place to wander around for while working up an appetite for some lunch or dinner. Depending on what season, you could see a harbor full of amazing yachts docked behind the resort. If you need some relief from the heat, you can always go inside and try your hand at the casino or meander the shops inside the resort.
One place I recommend for a quick bite and or a cold one, is across the street on the water. Its called the Green Parrot. Its a open aired bar on the water that has shirts and other signed items stapled to the thatched roof from past visitors. If you go, order the conch fritters and a sands. Its a great combo while you enjoy the breezes and passing boats.