If you ever though of visiting New York City in winter, then I recommend this:
A Winter Guide to NYC | A Cup of Jo. After you read it, you’ll want to head there before Spring.
I have been to NYC many different times of the year, and I found being there in December to be one of the best times to visit. In addition, going in January and February would be among the least expensive times to go. If you had planned to go mainly to see museums and shows and do indoor activities, then it could be the perfect time to visit. Of course you don’t just have to do indoor activities, as that lovely photo of people walking in Central Park in winter shows.
New York is great any time of year, but it can be especially so in winter. You should go.