If you live in NY and work in NY, then your income is NY source, even if the payer is out of state. Depending on whether you are temporarily visiting or permanently move to NY, you will owe NY either a non-resident return on your income earned while in NY, or you will owe a resident return on all your annual income from all sources.
Be careful about "I am interested in living in New York." Your domicile is where you live for tax purposes. Your domicile is your permanent home, it is where you have significant family, social, financial and legal ties; such as your doctor, dentist, church, bowling league, voter registration, and so on. There is no single factor that determines domicile, it is based on the combination of all factors. If you change your domicile to New York, then you are a NY resident for income tax purposes, even if you are physically in New York state less than 183 days of the year.
