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If your flight has been booked with RCI then they will take you from the ship direct to the airport - so you will probably be there mid-morning and have time to kill.
There is no tour you can take that will drop you at the airport that RCI offer. You can see if the airline will check you in early [doubtful] and then rush into NYC and back again but you will not have a lot of time.
We have not booked with RCI and have to make our own way to the airport.
On our cruise that we went on they arranged for us to use the hotel facilities that we stayed in on the day that we arrived in miami. Or the other thing that you could do is arrange a morning trip through the ship.
All I can suggest is find out if the airport you are using has a left luggage store and then grab a taxi into NYC to do whatever it is you want. I'd caution you to allow yourself plenty of time to get back to the airport because depending on what day it is, and time of day traffic can be a complete nightmare. If yu cant find a luggage store, i really don't know what to suggest as it's not much fun, sightseeing with luggage, unless there are a few of you, you could consider pre booking a limo for a few hours, get it to drive you around manhattan or whatever you fancy seeing, go for a nice meal and then hed back by taxi to the airpor.
So what airport are you flying from - EWR or JFK? You will still have the luggage problem to deal with as there are no left luggage facilities anywhere [fear of terrorists]. You can easily get into Manhattan from Bayonne - take the PATH [as sort of underground] from Hoboken and you come out right by Macy's.
Alternatively find a taxi company that will include some sort of tour and you can put your suitcases in the trunk [boot.
Sometimes if you have a late flight there is an excursion available through your ship eg city tour then RCI arranges your transport to the airport,check you booklet of excursions for availability or at the excursion desk on board ship do not worry as RCI departures go like clock work and they will get you to the airport on time whatever you decide to do Regards Iren.
RCI do not have a NYC tour that ends at an airport.
This has been my only complaint with RCI. You have to disembark so early and this applies at any port and if you have booked your flights through them you are left to sit it out at an airport where you have to be with your luggage until you can check in and there is not much chance of getting booked in more than 3 hours before your departure.
We faced the same situation 4 years ago and shared a day room in a Days Inn on 8th Ave with other cruise friends where we could leave our baggage, explore New York and freshen up/ rest prior to the flight home. We also booked transport to JFK from the Hotel, quite cheap too.