Ice skating either at the Rockefeller Center, Bryant Park, or Central Park is great fun for the kids.
ToysRus is fun, or even better is FAO Schwarz on 5th Ave, they've got the floor piano from the movie Big, and give demos on it, and the kids get to have a go.
Dylans Candy Store brought out the big kid in me!
And if your children are, or were, into Winnie the Pooh, the original Pooh Bear, Eeyore et al are on display in the Public Library - it was the highlight of my trip, but I'm quite sentimental.
There are some lovely Christmas markets, at Bryant Park and in Grand Central, but I'm not sure if they run through to New Year.