I agree with RGR, that anything in the theatre district is set to get you in and out in time for the curtain. Joe Allen and Orso are always reliable, although not spectacular. We like La Locanda on 9th and 50th Street, a bit off the beaten path but warm and food is good. Also, the Thalia on 50th and 8th, has a nice vibe (although my husband is a lunch regular and that could affect how we are treated.) The salad with sashimi tuna is great, and their polenta with mushrooms is fab.
Most restaurants in the Theater District are geared up to get pre-theater patrons out in a hurry. In fact, that's why people who are looking for a leisurely meal are cautioned to reserve after 8 to avoid the rush and crush. That said....
If you like Greek food, we've always found the service at Uncle Nick's to be swift. I wouldn't order whole fish because it usually takes at least 40 minutes on the grill. But lots of other dishes come out in a flash. It's on 9th Av., b/t 50th & 51st Sts.
Cascina, on 9th, b/t 45th & 46th Sts., can get you out quickly. Delicious Italian food, especially the first-rate pastas. Or you could opt for their pizzas.
Grab a great burger at the burger joint at the Parker Meridien Hotel. It's on 56th between 6th and 7th, so while not in the Theater District, it's fast enough and close enough that even with your time constraints you'll have plenty of time.
You can also try the Hourglass Tavern, on 46th between 8th and 9th. Do they still turn over an hour glass when you sit down? Either way, this places raison d'etre is to get you in and out fast.