Little italy NYC
I don't know if you wll find "fine" Italian dining in Little Italy especially while the festival is going on.
Most of the restaurants have good food and service.
I've never been disappointed at Il Cortile (Northern Italian), Da Nico or Puglia which has a great festive atmosphere and you eat family style.
164 Mulberry St, New York, NY 10013
125 Mulberry St, New York, NY 10013
189 Hester St, New York, NY 10013
The Village and East Village beckon, just a bit north and west or east, respectively, of the northern limits of the San Gennaro Festival on Houston St. How much are you looking to pay, and what would you like to have? For example, would you be satisfied with a good pizza-centric meal or would you rather go to an establishment that serves a wide range of items well?
My feeling is that Little Italy is always horribly crowded with tourists and really tacky, and that it's the worst around San Gennaro, so the thing to do is just walk up Mott St. for the experience and eat elsewhere. I do agree with Motosport on Il Cortile if you decide you really aren't willing to walk several blocks away from the area, though.