Governor's Harbour is a historic town about 5-1/4 miles SE of Alabaster Bay. It was once the Bahamain seat of government and may very well have been one of Eleuthera Island's pirate hangouts back in the 18th Century. The town has brightly-colored houses lining the hillsides, giving lots of visual texture to the area. The architecture is relatively unique to much of the Far Bahamas: at least from the water, many of the homes look like 19th Century New England style cottages. Governor's Harbour is very popular among cruisers for all the usual reasons - provisioning, things to do, and places to see.
Of course, I'm the schmuck who neglected to take pictures so you'll just have to get there and see for yourself.
The government dock has a deep approach and is busy with commerce - at least in late January 2014 when we stopped by. Governor's Harbour is an official port of entry and one I would recommend using for any official business. The bureaucrats there take it easy on the average tourist.
We did not anchor in the harbor but saw 2 boats there on the morning we visited. We've heard many other sailboats discuss anchoring there over the VHF radio, and we never heard of anyone experiencing problems. In contrast the cruising guides warn that the harbor bottom is scoured clean of most sand; thus they report that the holding is poor. I venture to believe that like many other Bahamian anchorages, it may be that in Governor's Harbour the quality of your anchoring experience depends on which spot you select to drop the hook, and which way the wind happens to be blowing.