Live in New Jersey Work in New York City?

I want to know if there are specific tax advantages if one were to live full-year in New Jersey and work in Manhattan versus the case where one were to live full-year in New York city and work in Manhattan.

If I were to live full-year in New Jersey and work in Manhattan, will I have to pay New York city taxes? I went over form IT203 (Non-resident income tax return); it appears that I will have to pay New York state tax and Yonkers nonresident earnings tax, but there is no provision for New York city tax. Could this be a potential tax advantage over the case of living full-year in New York city and work in Manhattan? It is a decent saving.

Furthermore, if I were to live full-year in New Jersey and work in Manhattan, will I be withheld taxes from New Jersey state, New York state, New York city, and Yonkers?

I actually don't understand Yonkers. What is it? Is it a defined boundary or region in New York city where one work? If I work in downtown Manhattan, am I part of

Live in New Jersey Work in New York City?

I can't answer all of those questions, but I can give you a little bit of information.

If you live in New Jersey and pay taxes another municipality or state in which you work (such as New York state, New York City, Yonkers, Manhattan), the taxes you pay to the places you work are deductible from your New Jersey income tax. In other words, whatever you pay to New York state income tax, New York City wage tax, Yonkers non-resident earnings tax, etc, is deductible from your New Jersey income tax if you live in New Jersey while working in New York.