A couple of places come to mind:

Trattoria Trecolori (www.trattoriatrecolori.com), on 47th between Broadway and 8th, is a terrific, mid-priced, Theater District Italian. It will be very lively until the theater-going crowd vacates, but you can be as loud as you want all night long.

Le Zie (www.lezie.com), on 7th Avenue near 20th Street, is a great, neighborhood Italian. No tourists here, just locals. But great, well priced food (including amazing spaghetti and meatballs) and a lively vibe.

East 58th Street has a couple of great places, too, including Felidia and Bruno's, but these places are likely to bust your budget.