Ahh I go to NYC a few times a year, grew up in the 'burbs and we go when I go back to visit!
For Broadway shows, find out which ones you want to go to ahead of time - especially if they're popular ones. OR if you like to be surprised, go to TKTS
in Times Square and buy half priced tickets- that in itself is an experience! You can almost definitely get Christmas Spectacular (Rockettes) tickets there also.
You're romantics, eh? How about a moonlight horse and carriage ride in central park?
What else do you guys like to do?
RE: Christmas windows- Macys! They used to do an awesome display inside too but when we went this year, it wasn't there... so check first. We went to Barneys and that one wasn't that good this year. Lord and Taylor- liked. You can usually find reviews of the displays ahead of time. In my experience they're not always consistent.
The tree doesn't go up until the 28th but that's definitely something to see if you're still there, depending on when Turkey day falls.
South Street Seaport is a fun place to walk around and people watch.
Then all the touristy fun stuff- statue of liberty & ellis island, empire state building...
The boat tours are also a lot of fun!