Hello,
My husband works in NYC but we live in NJ. His W2 shows only NJ taxes. Should we have paid NYC taxes? How do we fix this?
Thanks

No he will not pay NYC taxes as he does not live in NYC. He must report the income to both the states.
If you are present in a state, then any income earned during this period, must be reported to the state.
To your resident state, you must report your worldwide income for the year or for the residency period. If you paid taxes to another state, then you will claim credit for those taxes.
Read: Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)