There's lots to do in and around GTown/Elizabeth Harbour, including beaches, bars, snorkling, hiking, socializing, etc...(circumnavigation Great Exuma Island isn't one of them). With just a week, you'll probably stick pretty close to there, or maybe Long Island
, although the island chain to the NW is some of the best cruising in the world, IMHO.
You would need to get out on Exuma Sound (the ocean, basically) to get anywhere, and that may require the right conditions, depending on your sea tolerance.
Have a great voyage!!