I've lived in NYC all my life and I cannot think of any nurseries/garden centers that might sell figs in NYC...that's if you mean in Manhattan, specifically. If you are driving, and don't mind a little traveling, Bill's Figs in Flemington, NJ would be about your best bet. Some garden centers in Queens, on Long Island, and in Westchester County might have a small selection of varieties, but after the freezing winter, most nurseries might be sold out. Even if you manage to find any retailers selling fig trees, you are likely to get only "Brown Turkey"; "Peter's Honey"; "Celeste"; and "Kadota".
New York City, proper, is not really the place to go fig shopping. Sorry I couldn't help you with your fig quest. Enjoy your visit.
Frank