I work in NJ but live in NYC, do I get to take a tax credit and to which state should I file for the credit NY or NJ? How is this credit computed?

[TomD8]

You file a non-resident NJ return in addition to your home state NY return.  You'll be able to take a credit on your home state NY return for taxes paid to the non-resident state (NJ).

In TurboTax, complete the non-resident return before you do the home state return, so that the credit flows properly.

This FAQ explains the process in TurboTax: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return