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Try transatlantic aboard the QM2 - it's a classic sailing & you'll never be bored - the ship is the biggest afloat - you don't feel any swaying - it's like being on land! When you get to New York you'll be raring to go. I can't help you with prices - best just do a search on this website using the info I've given you & call cruise.co.uk to check. Good luck.
If possible I would do it the other way that way you get less Jet Lag and dont loose a nights sleep.