The usual anchorage is beside the moorings in front of the distillery. However, my preference is for a more secluded spot a little further up the Sound of Islay that is quiet and out of the tide.
If you want to go ashore to visit the distillery, then obviously that is where to drop your hook, but if you are just waiting for the tide to turn, or want a quiet night, then I know which I would choose.
This is Bunnahabhain from the North of the Sound of Islay, as you would see it sailing to/from Loch Tarbert:
Anchor in clean sand behind the spit, out of the tide: