Radio City Rockettes
Museum of Natural History
Metropolitan Museum of Art (their Xmas tree is gorgeous)!
I would hit the TKTS booth and see if you can get a deal on tickets for Annie, Cinderella, or Newsies. The Lion King is amazing if you have not already seen it, but I do not recall ever seeing tickets for it at the TKTS booth.
For food, I would suggest Shake Shack for burgers, etc. (theater district location) and Don Antonio (Neapolitan pizza, delicious to both foodies and non). Would they go for Esca (upper mid-range Italian, but DD could get pasta and DH could get basic fish)?
Dress warm!
DS - "The Biscuit" 8/11
Forever ours 4/12!