As a resident of NYC working in NJ for part or all of a tax year, would a person pay income tax to NJ for income earned in NJ, and also file for a credit in regard to NY income tax liability for income that was subject to tax by NJ?

As a resident of NYC working in NJ for part or all of a tax year, would a person pay income tax to NJ for income earned in NJ, and also file for a credit in regard to NY income tax liability for income that was subject to tax by NJ?
When you file NY return you will receive a credit for part and/or all taxes paid to NJ.

Agreed!

However, you need to have money withheld for BOTH NJ and NY state, as well as NYC.