Security is always an issue in the Bahamas. Although there is very little violent crime, common theft is always a problem. Some places in the Bahamas are worse than others with Nassau (New Providence Island) and Freeport (Grand Bahama Island) being the worst. A place that is one of our favorites in the Bahamas and one that you might consider is Harbor Island. It is off the North East corner of Elutheria. Between Harbor Island and Elutheria there is a very large sound that can accommodate many anchored boats and in many places is very good holding. It is easy to take a short ferry (10 - 15 minutes) from Harbor Island to Elutheria and pick up a cab ride to the Elutheria airport. Harbor Island has the casual atmosphere of a "family island", but is large enough to have resources like restaurants, bars, hardware store, small grocery stores, nightlife, etc.
To get to Harbor Island you must first go to Spanish Wells and hire a pilot to take you through the "devils backbone" - a congestion of coral heads a reefs to Harbor Island. The fee is small and conversation with the pilot on the way makes the trip interesting.