I'm a big fan of Lupa.

In Little Italy be warned that most of the restaurants are really bad. There are probably some good ones, but most aren't, so be sure you have a good, specific recommendations.

I've also been to Patsy's on 56th and was unimpressed. If you have a Sinatra fetish, I guess it can be fun (it was his hangout), but if it weren't for its association with the man this place would have closed decades ago. It's the kind of place that in many small US cities would be considered top end Italian, but in NYC there are many, many places to go that have better, less-expensive, more interesting food in a less stuffy atmosphere.