Thx Arthur. Re Caribbean, the OP did say "not too far, so Europe, maybe somewhere where we can wear t-shirts in December, just for a week or so".
West Indies would indeed be nice and warm, sunny too, unless you're jinxed and meet a Hurricane? BUT -- it can be a culture shock (you get to see the 3rd World), and many of the Caribbean cruises would involves starting and ending in Port Lauderdale, so you'd have to get though the wretched USA Home Security, and occasionally massive airport queues.
PLUS -- depending if the gestapo hired by the geriatric orange baboon decides if you're a potential immigrant or terrorist, you may not get in the country at all, quite an expensive business? Best NOT try to visit USA until they return to some form of established sanity and elect someone the rest of us can get along with?
Oh, yes, lots of possible cruise bookers, massive amounts of advice, see IGLU for a booker, or SAILAWAZE (plenty more), and Cruise.co. UK for advice galore.
Do beware some short cruises, which can be 'party' outings that time of year, 3 nights or so up and down the Channel.