I live in New Jersey and have taken a job in New York city. What taxes should my employeer be withholding from my check?

Withhold ONLY NY state income taxes.

Since you do not LIVE in NYC, you are NOT liable for NYC taxes.

NJ gives you a credit for the taxes you will pay to NY state. Since NY state income tax rates are HIGHER than NJ, that credit should completely offset whatever NJ taxes are owed, so withholding NJ taxes is a waste of time.

You WILL have to file both a NJ and NY state income tax return.