We do the last week of September every year (birthday time!) THe weather is wonderful. You do have to realize that you are in the middle of hurricane season, and the ship doesn't always go where you are planning to go. The captain will head away from any hurricane or tropical storm patterns. We went to Key West before the Western existed. We've never had to miss Castaway, although we did miss some other ports of call. On one cruise, we missed St. Maarten, on another we missed Grand Cayman. However, they try to arrange alternative ports or activities, and we always have a great time. I'd be upset if we ever missed CC, but that hasn't happened.
I like Sept. much better than summer. THe weather is warm, but not opressively hot or humid. Water temps are good for swimming, and the prices can't be beat!