The best restaurant I have been to in NYC is Blue Hill located 1/2 block from Washington Square Park. The food is spectacular along with the service and the Wine Vixen, Claire is absolutely spot on when recommending wines.
Blue Hill | Blue Hill Farm The atmosphere is quiet and romantic, hard to describe it but I go there every trip to NY. Get reservations early as it is generally booked. Ask for a corner table in the front dining area.
Another place to go for lunch is the Shake Shack at Madison Square Park. Great burger and fries. The Shake Stack shroom burger is the best IMHO but all are great. The is just one of Danny Meyers successful restaurant. They sell $4 million a year from this location alone.
Shake Shack
Another place to stop is Pommes Frites and get some Belgian fries. Located in the east village. Had to go there several times during the week I was there.
Pommes Frites Inc./Menu
One last place at least to look at is The Spotted Pig which is in Greenwich Village and is a gastro-pub. Great food in a pub atmosphere. It is one of Jamie Oliver's restaurants.
The Spotted Pig - New York
I have been to all of these and have no reservations about recommending any of them.