Junior's is awesome! Best cheesecake in the world. Best deli-Second Avenue, IMO. Formal teas- Pierre Hotel, Plaza Hotel. Slavic restaurants in East Village. 2nd Ave has a strip. Greenwich Village - Elephant & Castle on Greenwich Avenue, Pete's Tavern, Waverly Inn. Bars - Oak room at the Plaza, Carlyle Hotel bar, 30 Rock - can't think of name right now. Will recall.
Lincoln Center area has great restaurants.
Basically, the idea is to do ethnic and where NY residents would eat. SoHo also has awesome restaurants. The New York Times and NY mag have decent reviews.
It is restaurant heaven. Junior's Cheesecake is way up there. the 2nd Avenue deli's corned beef and pastrami sandwiches are unbelievable. The mushroom barley soup and chicken noodle soup are art forms.
I like the main restaurant at the Metropolitan Museum of Art and the Museum of Modern Art. The cafeterias stink.
Olives, just north of 14th St., has great food and a bar. Pricey but worth every penny. Great European and resident crowd.
Asti's in Greenwich Village. The waiters sing opera to the customers. Food is mediocre but it is the show.
Restaurants open and close quickly. Word of mouth is good.
Balducci's, Dean and DeLuca, and Zabar's have great food.
Barney's Restaurant had a fantastic restaurant.
Sidewalk vendors can have good food.
Windows on the World had fantastic food and what a sight. It was my favorite.
I would stick with local paper reviews. It changes all the time. A lot of people like the Korean grocers for food. The grocery stores tend to stink. I lived in Greenwich Village. People shopped European style, buying bread from the bread baker, coffee from the coffee shop, etc. I only bought cereal and milk from a grocer. An exception is the A & P on 14th st. You need subsidized rent for a decent grocer.