New Jersey and New York tax income differently because NJ wages some benefits that NY does not.
Because of that, you should prorate your NY income by days, as you have done, and not use NJ W-2 wages.
Nonresidents of New York City do not pay NYC income tax so do not claim a credit for NY state tax.
Your NYC tax should only be for your period of NYC residency. If your employer continued to withhold NYC tax after you moved to NJ, the excess will be added to your NY refund.
For example, if you lived in NY for 6 months and had 8 months of NYC tax taken out, your NY tax return will only show six months of NY and NYC income but 8 months of NYC withholding, so the difference will be refunded to you.
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