There is a public beach within a block or two of the Sandals Resort on Antigua.
Get off the ship, pick a taxi driver and tell him to drive you straight to Sandles.
I'm not sure but it is entirely possible you coul just walk around the side of the resort and voila - there's the beach.
Of all the places I have ever seen or been in world that is the single most beautiful spot.
My next vacation will be to go straight to the Sandals on Antigua