When I went to NY in January, my 10 year old stepdaughter came, too. We were only there for a short period of time (in transit to the actual place we were going), but she loved it! She even made herself a little NY photo album.
I have to say, I had to go again last summer for work, and it was so much nicer in the winter - cold, but much less crowded and much prettier. Plus, I think travelling with kids who think everything is cool is much more fun than travelling with adults who complain about everything!
Here are some things she really enjoyed (not in any particular order):
1- riding on the subway
2- the Metropolitan Museum of Art (which surprised me - I thought she'd be bored silly. Granted, we only stayed about an hour, but they had a really neat fashion exhibit about clothes made out of or inspired by animal furs that caught her attention)
3- Central Park. She LOVED central park. We took a million photos. It's really pretty in the winter.
4- We went ice-skating near Rockefeller Plaza. I don't know if it's open in November, but if it is, you should go. It's a bit expensive but really fun. It was my stepdaughter's first time iceskating, but we had a blast! Now, everytime we see a movie and someone goes iceskating at Rockefeller Plaza (which happens more than you'd think in movies, for some reason), my stepdaughter grins and says, "I was there!"
5- Times Square at night! It's incredible! All the lights really take your breath away. For kids, that in itself is neat, plus there are a lot of shops. The Toys R Us there is huge and has some funny gimmicks inside other than just toys to buy (for example, a Statue of Liberty made out of legos).
