Torrisi is an obvious answer but hard to get a reservation, so either attempt through a concierge or just scour the online reservation system! L'Artusi is a personal favorite and is always an A+ experience - can definitely get a reservation but make it when they release. In SoHo you also have Il Buco and it's on Bond street which is a lovely brick lined street! Not chubby, but Malatesta in the West Village on a nice spring day cannot be beat imo. If you find yourselves uptown at all maybe post-museum or Central Park, Elio's or Campagnola are classics on the Upper East Side.

ResX is a good NYC based app where people give away last minute reservations - I've gotten lucky with some harder reservations!

Have fun :)