The beach by Atlantis on Paradise Island is beautiful. If you take the tour of The Dig it includes the use of their private beach, just not their pools. They have parasailing, jet skis, etc available at that beach too for a reasonable cost. You'd need to take the water taxi across for $3 pp each way (or a regular taxi for about $5 I think) and then you can walk to Atlantis.
Sovereign of the Seas, Royal Caribbean 11-17-03
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Sovereign of the Seas, Royal Caribbean, 9-24-07