Asking if there are cute restaurants in New York is like asking if Starbucks serves sugary drinks :) I'm sure you can find many but here are two suggestions, Pio Pio within a 15 minute walk is a high quality restaurant and then Juniors literally around the corner is a diner and a New York City must. The cheesecakes are big enough for 3 people. Don't forget to go to Catz deli another day.
Well a couple of blocks away you could get some really good food, also there are alot of middle Eastern food carts where u could get kebabs or chicken rice. Enjoy.
Yes there are several in the immediate vicinity. There is a nice quaint restaurant next door.
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