"Old school" Italian cuisine
In Little Italy... not really. You could always go for the home cooked style foods served at Frank (2nd avenue at 5th) and Max (Avenue B). Il Baggato is always good, but I believe they are closed for until after Labor Day. Bar Pitti on sixth avenue also serves some very good pasta.
Nowhere south of 14th St.
Gino Italian Cuisine, Lex between 60 and 61. See previous posts on the subject.
Patsy's on 56 between Eighth and Broadway
Andy's Colonial as a previous poster said
Parkside Restaurant in Corona (Corona and 51 Ave) if you're willing to travel
Valentino in Yonkers, Bronx River Road just off the Bronx River Parkway north of Woodlawn
the key: travel
For olde Greenwich Village (its own Little Italy in the not-too-distant past) try the Minetta Tavern, 113 MacDougal St. (bet. Bleecker & W. 3rd Sts. at Minetta Lane), 475-3850.
It's been there since the 1930s, and the walls are packed with old caricatures and pix of owners with fighters, movie stars, etc.
My only beef is that the bar now blasts crappy music, tho sometimes it's bearable Italian pop (and if you sit in the dining room you're shielded from it).
Anyway, they've modernized the menu a bit, but most old style dishes can be found. My favorite linguini & clam sauce -- the clams taste roasty instead of just steamed.