The Caribbean of course! Not only is it much cheaper, but the culture is much more vibrant and open to passing through tourist. You have so many activities you can do in the islands for free that would cost you more than a few pretty pennies in the med. Anchorages were a good point, still many places in the Caribbean that are free. Of course, if you do go to the Caribbean try to stay out of the major areas as they WILL find ways to get as much or your money as they can.
If you do decide to go to the Caribbean, visit the out islands. It will be like taking a trip back in time.