We had a similar dilema when we arrived in New York in January this year on the Queen Mary 2. However Cunard had a trip offer, of a coach sight seeing tour of Manhattan with a stop for lunch and then drop off at the airport. Each coach was geared by both airport and departure times, luggage was therefore not a problem, you had a quick glimpse of all the main sights and arrived in time for your appropriate flight. The cost was about $90 per person (£45 a the time) but well worth it for the peace of mind. Wilba is right, there is no way you could get to any airport and back in the time frame you are talking about, also if you are arriving in January snow disruption could well occur and our cold weather is nothing at all compared with theirs, so make sure you have plenty of thermals.
The best option would be to hire a taxi or van for the day & let them take you & your luggage on a tour of New York. The journey to & from the airport twice, be it JFK or Newark in the traffic would just not be practical in the time frame. Of course an even better option is to fly home the next day. Regards Wilba.
We hired a limo. They met us at the pier side, we put the luggage in the trunk and they did us an all day tour holding the car when we wanted to jump out. We had a great driver and it worked really well. The concierge service on the ship should be able to recommend specific companies that they have validated.
We had a similar problem at miami this december. cunard however did offer excursions for the day stating cases would be kept on the coach until we were dropped at airport. they also offered complimentary airport hotel where you could leave cases and have complimentary lunch.
we opted for the free lunch thinking we would get a cab to the sights of mimai ourselves but when we got on the coach we were suprised to be told cunard had arranged a free tour of fort lauderdale and miami and a stop at a shopping mall as well as a free lunch - this was great .... we did later however find our why they done this as every cruise passenger has special screening at mimai (this may be the case in new york too) - it took 3 hours from arrival at the airport to getting through security!!! we the found our cases had all been broken into and searched. check TSA before you go!