The address on your tax return is only the place where you want to get official tax-related mail. It does not have to be the place where you live.
You will generally owe state income tax to the state where your permanent home is located, even if you don't physically live there. This is also called your domicile. You only have one domicile at a time, even if you have multiple homes. There is no single factor that determines where your domicile is located, but some factors that are important include where you have professional relationships (doctor, dentist, attorney), where you have family and job, where you have significant social relationships, where you have a a drivers license and voter registration, and your intent to return. Also, to establish a new domicile, you must take active steps to abandon your prior domicile.
So you need to look at the facts of your own life. For example, if you lived at home with your parents before joining the cruise company, you return there on holidays, you still have personal belongings in your parents house, and so on, then you probably are still domiciled there. You never took steps to move out, to abandon your domicile, so you could still be a resident of NY for tax purposes. On the other hand, suppose you moved to Florida, got an apartment for 3 months, then decided to go cruising. You definitely moved out of your parents house in NY, and when you joined the cruise, you just sold your used furniture and stuff and walked away from the apartment. That sounds like you abandoned your NY residency.
It depends on the facts of your own life.
