Yes, you will get credit on your New York tax return for the tax that you pay to New Jersey. It's called the Resident Credit.
You will have to file two state tax returns, a New Jersey nonresident tax return and a New York resident tax return. The New York tax return includes both New York State and New York City taxes. You have to pay New Jersey tax on the income you earn in New Jersey. Since you live in New York, all your income is subject New York tax, no matter where the income is from. You will get the Resident Credit on your New York tax return for part or all of the tax that you pay to New Jersey, but you will still have to pay some New York tax, because the New York tax rates are higher. As Critter-3 said, prepare your New Jersey nonresident tax return first, then your New York resident tax return, to make sure that the credit is calculated correctly.
