Steve - As mentioned I would be cautious about overnight anchoring in Savannah Bay. It can become quickly dangerous if a swell moves in. Also red-lined by some charter companies, though I don't recall Moorings policy.
White Bay at Guana Island has 15 mooring balls (as of early December). Anchoring is possible - just make sure you get into sand not the reef. The bay is exposed to northerly swell and can get lumpy in strong winds.
Peter Island offers several excellent north and south shore bays for anchoring.
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