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JFK to Manhattan is a fixed flat rate cab fare of $45.00 plus any tolls. (plus tip of course). Cape Liberty cruise terminal is in New Jersey, and this presents a problem as cabs from NY state are not allowed to pickup in New Jersey (it is like a cab from Essex not allowed to pick up a passenger in Suffolk) - so the cab will take you there but he will charge you for having to return to the city empty. It is approx $98 from mid-Manhattan to Cape Liberty using a limo service. You can find one on the internet.
We paid roughly $60 from JFK to Manhatten and approximately $55 plus $10 tip to take us from our New York hotel to Brooklyn Cruise Terminal. This was March 2008 so prices may have increased slightly. However all taxi prices are published and regulated but do ask before getting in one (please ensure that this is a bona fide yellow cab) You can also pre book your transfer by limo via the UK if you place a search for airport transfers for the USA. Hope this helps.
Have you thought of 'Blue Shuttle', (Google it). We have used them from /to Liberty/Manhattan Hotels/JFK. They use 12 seater vans & the cheapest way is a 'shared ride' which means they may have drop offs on the way. We have used this service & it works out quite well. It's about $20 per person a ride.