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).

If I live in NYC, but work in Westchester County, do I need to pay for the NYC income tax? Or I'll need to pay both income tax in Yonkers and NYC?

Nope just NYC

What if you work in Yonkers, but live in NYC? Do you pay both Yonkers and NYC? 

@jasonortiz96 --

See "Individuals with Yonkers income" in this NY tax reference:

https://www.tax.ny.gov/pit/file/nyc_yonkers_residents.htm#:~:text=Individuals%20with%20Yonkers%20inc...

That doesn’t answer my question. It’s a simple yes or no question. 

@jasonortiz96 --

The yes/no answer is Yes.  You will pay the NYC resident tax and the Yonkers non-resident tax.