Alabaster Bay is a broad bight about 10-1/4 miles SE of Hatchet Bay. It is open to winds from any westerly direction but the depths are good. Holding varies; the first visit there in January 2012 we picked up a large rock on our first anchoring attempt but we held in hard-packed sand on our second try. East wind was blowing at 10-17 knots. Our second visit was in January 2014. We anchored fairly far off shore with about 9' under the keel - again in hard sand which presented no problem to us in a NE breeze at 8 knots and less.
Given the varying bottom and hard sand, I would avoid Alabaster Bay if the wind were blowing from any westerly direction above 10 knots. Strong winds from due north or south might also be problematic. There may be a large number of commercial crab pots and floats near the approach to the anchorages in Alabaster.
However, if the weather and the anchoring conditions are good, Alabaster has a nice long beach to explore in front of Cocodimama, a small resort shown in that pic up there on the left, and the public-access road; both times we've visited there have been local folks spending the day swimming and picnicking on the fine-grained sand beach. If recent Bahamain history interests you, there is a short excursion of about a mile to the ruins of a former US Navy base from the 1960s-1970s, overlooking a beach on the Atlantic side of the island. That's the Atlantic beach view on the right, there; the Navy ruins are behind the camera and back up a low escarpment.
GB even found a voodoo shrine complete with bottles! Skulls! And candles! upstairs in one of the abandoned Navy buildings.
...And we survived to tell the tale...