We live on Long Island and go into the city quite often. Even more trips to the Bronx to go to Yankee Stadium but, I will keep on topic...lol.
We love the Bronx Zoo. Lots to do and see. It has a great bug carousel, a monorail ride and a sky ride. (Like WDW used to have). Then there is the butterfly garden, Tigers, Monkey house to name a few, and it has a wonderful childrens zoo. It is defiantely a lot of walking and a place that you would need a full day for. We are big Bronx Zoo fans.
As others have mentioned, the Toys R Us store is great, make sure you take a ride on the ferris wheel. We always hit the
Disney store, American Girl Place and the Hershey store.
The kids love to see a show. We usually go in to see the Christmas Spectacular each winter but, we are going to see The Little Mermaid in a few weeks and can't wait!
Times Square is a favorite of my kids. They are 10,8 and 4. Someone else mentioned the Naked Cowboy...my DD 4 is always the first to spot him...lol.
Lots of great things to do with kids as you can imagine. Have a great time!!