I would look into a Celebrity, Princess or Holland America cruise - i think these lines would suit your needs. Most cruises from the eastern seaboard would only get you to the Bahamas and part of the Eastern Caribbean. Look into departures from Virginia or the Carolina's to save you some air time.
I like more sea days as opposed to port-intensive cruises, myself. I find that port intensive cruises aren't that relaxing.
What are your interests when it comes to the islands? Give us some ideas so that we can make some specific recommendations.