If you like the idea of all mod cons and luxury yet in a 4 mast schooner (peace and quiet while you sail too)- try Windstar. You can even help sail her if you want!
Simple - Azamara Journey for 12n - pure luxury and no ankle biters - look at their itineraries out of Miami.
Try the QM2 Cunard pure indulgence if you can go the Grills and the Islands arent bad either we went late Feb this year extended stay in NY before and after although very cold but the cruise more than made up for it.
A small point, but no matter which ship you select, get a balcony and you can sit there in glorious isolation with the sun beating down, a drink at your side and the ability to slip back inside for ablutions or a kip whenever you want.
As far as the itinerary is concerned, watch out for RCI who have a habit of substituting a day at sea for an island AFTER you've booked.
P&O Artemis - 23 Jan - 7 Feb.2010 - 10 Caribbean Islands, definitely child-free. Ok so she is not a new glitzy whale of a ship, but she is comfortable, friendly and just the right size. Thank goodness P &O have two child-free ships, the other being Arcadia, more modern and larger, but at that time she will be off on her world cruise but definitely worth considering for some peace and quiet away from the screamers another time.