The only two NY cities that have a separate tax are Yonkers and NYC. Yonkers taxes you if you live or work in Yonkers, but NYC only taxes you if you live there (you are not taxed in NYC for your work performed there).
If you live in Yonkers and work in NYC, you will be taxed by Yonkers on your NY State return for your Yonkers residency. You will not be taxed in NYC for working in NYC. (If you live outside of Yonkers and work in NYC, you will not be taxed to either Yonkers or NYC).
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