Near The Plaza Hotel
A quirky little place that serves food quite late (2am?) is Park Blue. They are on 58th (the back side of the Plaza) up a block and a half across the street from the back door of the Essex Jumeriah Hotel (you could walk up Central Park South/W59th St, duck into the Essex, and walk through and come out the back door.
The food is all small plates, and it's pretty good. The wine list is good, and strangely it's all half bottles. Cocktails are also good, try the chocolate martini, it's like dessert.
Farther over, at Columbus Circle (corner of Central Park South and Central Park West) in the Time Warner Center, Landmarc serves food till 2am. Menu is has highs and lows, virtually all of the salads are great, the steaks are good (but the salad that comes with the steak sucks) the oysters are good, mussels are good, pass on the pastas, chops are good, the fish is fine but the accompaniments suck, the sides are good. French fries good if hot which is 1/3 of the time. Wine list is good and not marked up a lot.
Park Blue is a funny little lounge, give it a try. Landmarc is a big factory, it's OK.
Burger Joint in Le Parker Meridian Hotel on 57th at 6th Ave is open till 11:30pm but you might call ahead to be sure.
118 W 57th St, New York, NY 10019
10 Columbus Circle, New York, NY 10019
158 W 58th St, New York, NY 10019