You want Italian food and you're in New York City... that narrows it down to about... I don't know... a million choices. I'll narrow it down to ONE for you.
Vincent's is on Mott St in the heart of Little Italy and surrounded by all the Italian-American culture you can stand. It's just north of Canal street and around the corner from Mulberry, which is the place to be during the San Gennaro feast. You'll walk right in with hardly a wait if it's not during that feast, of course. But you'll go there again and again for the sauce; which, incidentally, you can buy in the jar as well.
Ok, it's not the fanciest place on the planet, nor the most expensive and maybe not even the best, but it's definitely a place that cannot be overlooked.