According to the British government, the outlying islands of The Bahamas, called the Family or Out Islands, are known to have lower crime rates. The Out Islands are all the Bahaman islands, excluding the main islands of New Providence and Grand Bahama Island (New Providence is home to around 70% of the population and most of the crime).
Among the Out Islands are the Abaco Islands and Eleuthera Islands. Since the 1970s, the Out Islands have also been called the Family Islands and are made up of around 700 islands (only some of which are inhabited).
The Abacos are considered some of the safest islands in The Bahamas and are known for being family-friendly. The Abaco Islands have only a population of around 17,000 and are made up of Great Abaco, Little Abaco, and several smaller barrier cays. See crime statistics in The Bahamas on the Royal Bahaman Police website.
So to keep safe while in The Bahamas, remain vigilant and plan on visiting the Abaco Islands. Naturally, the safest islands are uninhabited islands that one can rent as a private island. But when planning a vacation on the inhabited islands, plan on visiting the comparatively safe Abaco Islands.