Incorrect locality on my w-2

A while ago, when I got my w-2 from my employer, I went to file my taxes and I notices that my locality was written as NY City, and while i do live in New York State, I don't live any where near NYC. I then went to my employer and they got me a w-2c form but I am not sure how this process works. Under correct information it still says NY City. Do I need to request another w-2c or do I fill in my own information now? Anything will help, thanks in advance