Little Italy in Manhattan has been almost entirely absorbed by Chinatown. Very little is left, and most of what is left is very touristy. One notable exception is DiPaolo’s. Really top notch deli selling excellent cheeses, salumi, and other Italian foodstuffs.
Tacchino’s advice about going to Arthur Avenue is spot on. Do it. It’s a short and very pleasant train ride from Grand Central. The place still looks so much like the quintessential Little Italy that it is used for movies all the time. Mike’s Deli in the market makes a hero called the Yankee Stadium that is unreal. The little shops will give you free sampled of just made fresh mozzarella, sorpressatas are hanging from the ceiling, and the butcher shops will sell you a whole lamb, pig, rabbit or goat.
There are two prominent fish-mongers, both of which set up stands out on the sidewalk where you can buy freshly shucked oysters and clams to munch on between visits to all the great little shops.
Go to Arthur Avenue. You will love it.