Cruise and stay bahamas.
Please do not consider New Orleans. i was there Feb 2006. The first liner to dock after Katrina. Hated the place. The whole place was awful. Nothing opened apart from the French Quarte, which was really seedy and expensive. Maybe it is all sorted now, but I would not take the chance. Too many other places to visit in USA.
Depends how long youre going for. Normally there will be 2 formal nights per week where people are expected to get their posh stuff on, but otherwise its just smart casual or casual.