Tea and Sympathy
Describes itself as "a quintessential corner of England in the heart of Greenwhich Village", typically English meals are available here perfect for the Anglophile or homesick Brit!
Babbo
The most famous of Chef Mario Batali's restaurants, and especially well-known for its pasta tasting menu. Reserve a month in advance or stand on line before opening time 5:30 on weekdays and 5:00 on Sundays to try to get a seat at the bar or one of the tables kept open for walk-ins. Babbo is one of the hardest restaurants to get a reservation at in New York, which should indicate something about its popularity. Do not expect a cheap meal, but this is one you don't have to dress up for.
Blue Hill
An upscale American restaurant known for its fresh ingredients and subtlety. Call ahead for reservations.
Red Bamboo
Excellent vegetarian soul food, organic wines.
Lupa Osteria Romana
This is yet another restaurant associated with Mario Batali, but the Executive Chef is Steve Connaughton. This is a very good, relatively informal, mid-priced eatery, with a good and fair-priced wine list. Every fan has their own favorite dishes. First-timers may want to share several smaller dishes instead of having full meals, in order to sample the cuisine, but the primi and secondi are also worthy. The excellent Tartufo is their best dessert. Reservations recommended; otherwise, you may have a long wait.
You'll find hundreds of restaurants and sidewalk cafés of virtually every culture. All-American, Mexican, Indian, Italian, Polish, Pakistani, Spanish, Chinese, Thai, Vietnamese...the list goes on... At many spots you'll find affordable eats with the chance to enjoy your meal on the sidewalk. There are also some well-known upscale restaurants in the neighborhood.
Otto
The pizzeria in the Batali chain. Prices are much cheaper here than at Babbo, but the entire concept of the restaurant is different, so take it for what it is. The antipasti and gelati as well as the pizza are well thought of.