Got it, so if your employer isn't NY-based and you weren't assigned to a NY office while working remotely, only the income you earned while in NY would be taxed to NY. You'd only get a credit in NYC for the taxes you paid to NC if you had to report the same income on both returns, which wouldn't be the case for you. Instead, you'll allocate the income that you earned while in NC to NC and the income that you earned in NY to NY. Same of NYC.
Keeping your work address in NC means that your employer will likely continue to withhold NC tax even though you aren't living there (unless you can claim exempt from NC tax withholding).
You'd have to file a NC nonresident return and allocate $0 of income so that you can get a full refund of those taxes. You'd file a resident return for New York and have to pay the tax on the return. It would be best to make estimated payments to avoid a balance due for New York.
