We have just come back from spending Christmas in the USA. We were only there a week, which was enough for us to spending with family. We were originally planning a week with family and a week in the sun.
The ideas we had for the sun were a a week in Puerto Rico, or Key West, FL, or a four day cruise from the Miami area. Disneyland would have been fun but you can't guarantee hot. You have to be south of Miami for that. The gulf coast was hit by tornadoes on Christmas day this year, so even places that are pleasantly warm are not guaranteed good weather. We couldn't make up out minds what to do that we ended up doing nothing :(.
It's nice to have snow at Christmas (we had 8" on Boxing Day and the kids had a blast).
I have a big problem with city holidays with kids. The "must dos" in a place like NYC can be done over a couple of days - Empire State Building, Statue of Liberty, Central Park etc., followed by a museum and a look around some iconic areas. After that, my kids will say that all we ever do is walk the streets, going into shops and never buying anything. I think you need to pencil a rough itinerary of each day and think about what you will do when doing nothing (hang out in the hotel?). How will your 4 year old react to doing things over their head, or lots of walking, with jet lag?
The other thing to note about NYC is that it is a money-haemorrage. You can check out the prices of activities online, but you can easily spend $200 a day before food.