Usually passes the Statue of Liberty roughly between 6 & 7 AM depending on cruise itinerary and it will be on the port side.
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While departing NY, you will see it on the starboard side. On your return it will be on the port side. Usually the ship pulls into port before the scheduled arrival time of 8 AM. You will have to be up on the deck at least around 6:30 AM to see it when you pass in front of it as you arrive in NY.
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