+1 on Stardust Diner. The food was overpriced, but my out of town guests were paying for a bit of entertainment as well. If you don't want to get ripped off on food, walk to Ninth Avenue. Shake Shack isn't worth the wait on 8th Ave; there are other locations with shorter lines.
For Italian, Eataly by the World Trade Center was surprisingly good and had a nice view.
Christmassy Things to Do (not already mentioned):
1) Bryant Park is great with the markets and ice skating rink, and don't forget to peek inside the Public Library;
2) Grand Central Terminal is terrific, and kids may enjoy the Whispering Gallery (near the Grand Central Oyster Bar);
3) FAO Schwartz is resurrected in the Rockefeller Building