What is your criteria for best?

For many people it means huge plates of pasta & meatballs that are to die for (or from).

For others it's a place that has the traditional Italian restaurant menu - all the pastas, chicken, veal, & eggplant parmesan, saltimboca, etc - the same menu you'll find in a gazillion places

For others it's more modern Italian inspired dishes, but with some chef's creativity.

Babbo and Del Pesto, 2 Mario Batali restaurants are considerred some of the best by critics. Marea is another. Here's a Zagat list. http://blog.zagat.com/2012/05/new-yorks-12-best-italian-restaurants.html

We love this neighborhood place, Barbone on Avenue B.
Mario Battali's Chelsea restaurant on 10th Avenue at 15/16 is Del Posto.

I don't know if it is the finest, but Maialino is certainly very fine.

http://maialinonyc.com/

Key question: How much do you want to spend? Or is there no limit to the cost?

Best by itself means nothing. So what are the adjectives?

We are traditional and go for Babbo. but agree - how much do you want to spend - specific $ amount either for entree or whole meal with drinks and/or wine? Or, if you prefer, go to menupages.com to see the actual menus with prices.

Del Posto. (Bring money.)

Maria or Del Posto are the best in my opinion, but there are a lot of excellent Italian restaurants in the city. Maialino is great, but it only takes reservations 4 weeks in advance.

I see I mistyped r was auto corrected. It's Marea and specializes in fish. Of course it's also super expensive.