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The only major island (not counting the cays) that has ferry service from GBI is Abaco, and you have to drive 1 hour out to East End to catch it. Then it drops you off in the middle of nowhere and no taxis or buses are available at the pier, so you have to make advance arrangements. Smiling Pat will take you there on a day trip - www.smilingpat.com - seems expensive, but half the fee is the ferry tickets which run over $100pp RT.
Other than that, the only way to access any major island by boat is to contract a speedboat on a private basis with a company like Go Fast Adventures or Exotic Adventures, which is cost prohibitive unless you have several people. They'll take you to Abaco or Bimini.
There are a few cays off the ends of GBI, there are many discussions on them in this forum including a few in the past week or two.
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