In the Personal Info section of TurboTax, you should enter NC as your "State of Residence", and you should indicate that you also lived in NY. This will prompt the program to generate two part-year resident state tax returns. NY and NYC can tax all your income prior to your move; NC can tax all your income after the move.
See this TurboTax help article:
How do I file a part-year state return?
"For tax purposes my job location is NC even though I live in NYC so I'm paying taxes in both locations."
Did you physically work in NC while you were still an NY resident? If not, then you would owe no income tax to NC on your earnings during that portion of the year. NC does not tax non-resident remote workers.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
