Mr. Broadway
In midtown there is Mr. Broadway on 38th and Broadway, which is strictly Kosher and offers a full old style deli menu (their cole slaw is out of this world). It also has chinese and a sushi bar as well as Israeli meats and schwarma. There is of course over stuffed deli sandwiches.
They have a private room plus the main dining area. The ambiance was old world deli, however they just finished a major renovation which made it more modern but they still kept the vinyl couch seating in the main room.
It is my obligatory NYC stop when I come in and I will be there next week for supper.
Might be worth a consideration