We took our then 10 yr old dd & 14 yr old ds to NYC last year at this time. We toured the department store window displays at night and ended up at Rockefeller Plaza.
Took a walking tour of Central Park with the Big Onion walking tour. I was actually surprised how much my kids enjoyed it. They're not history buffs or bookworms, but they got a lot out of it.
Walked the High Line and ended up at Chelsea Market for lunch.
The Museum of Math was pretty cool. Also visited the Natural History Museum.