Remember that 20 blocks north or south is only about a mile. So don't panic if you don't see anything within a blacok of your hotel.
There are tons of pastry and coffee shops in the neighborhood of where you are staying (which sounds like the Helmsley Middletown Hotel). Names escape me. But, you just need to walk to the corner of 47th and 3rd for your morning joe and croissant.
There is a Carmine's in the theatre district that may serve up what you're looking for in terms of old school italian served family style in huge portions. it's kind of touristy as is it's midtown counterpart Tony's of Napoli. I like the food at Carmine's for a big group.
But, if you're looking for a real old school, gray haired, sport coat wearing New York Italian American place frequented by locals rather than tourists, I recommend Villa Berulia, about 13 blocks south of your hotel on 34th Street at Park Avenue.
They make a really great vodka sauce that they serve over penne tossed at your table. And frankly, they make the best osso buco I've ever tasted in my life.
Villa Berulia is old school and off the beaten path. The Babboo crowd will sneer at you for eating there because the food isn't modern and contemporary. But, it's damn good.
Villa Berulia
107 E. 34th Street
212-689-1970
www.villaberulia.com
Carmine's Theater District
200 W 44th
212-221-3800
www.carminesnyc.com
Tony's di Napoli (not recommended)
147 W 43rd
www.tonysnyc.com