If you are looking for famous places to eat in NYC that locals often eat. Come to Joomak Banjum!

A 2-min walk from the Empire State Building
Address: 312 5th Ave, New York, NY 10001. 
Get directions: mapquest driving directions.
Phone: (212) 268-7888
Reservations: resy. com
Joomak Banjum in Koreatown is not for the faint of heart. Their six-course tasting menu costs $180, but if you have the money, this is a great place to eat small, flavor-packed dishes that are executed to a high standard. 

Your meal will begin with custardy butternut squash layered with caviar and will be followed by a variety of other impressive dishes inspired by Korean, Chinese, and French cuisine. The squid ink sourdough jajangmyeon with candied Meyer lemon is a standout, and the cranberry tart topped with homemade Pop Rocks will transport you to the FAO Schwarz candy section. 
Bring a group, plan ahead of time, and make sure no one orders the same dishes from the tasting menu. That will be one of the most enjoyable fine dining experiences you've had in New York.