Both Moorings and Sunsail are available in the Abacos, and they are always a safe bet. However, my personal preference is to go with someone smaller. I've heard good things about Cruise Abaco, which might be locally owned (not sure). Also, Dream Yacht Charters has a base in the Abacos.

The charter bases are all in Marsh Harbour, which makes it easy to fly in. And there is a large grocery store (Maxwell's) to meet your needs (as well as liquor stores, a bakery -- gotta have Bahamian bread!).