We took DS to NYC for three days, when he was about the age of your oldest...
We stayed just off Times Square. Which I can recommend. My son enjoyed experiencing the hustle and bustle and lights... seeing it all in person.
(but would not want to be right on the main area of Times Square! Practice your double-time power walk!)
Agree that you need to be very aware of the accommodations and room size.
Maybe more people on the NYC board on tripadvisor could recommend places with rooms that can accommodate 5.
I think that even a 1 year old counts as another occupant, and would be subject to codes.
We took the first ferry of the day over to the Statue Of Liberty. Spectacular in the morning sunshine, before the crowds!
I do recommend going this early, or as early as possible.
We did make sure we had gotten our tickets in advance.
Also saw the new building going up at the site of 9/11.
We did Central Park, and the museum.
Went to Top-Of-The-Rock.
My son would have liked that double-decker bus tour. And, it might have been fun! But, on a short trip, and a budget, we didn't to this. Your family might enjoy it. And it would be a good way to get a tour quickly and easily.
We also did the F A Swartz Toy Store (spelling)
And, went to Good Morning America.
I actually think my son enjoyed seeing this in person, and shaking hands with George, seeing Robin, etc...
(Even though it was not a good day to be there, as the weatherman and regulars who work the audience were out that day...)
It was a really wonderful trip!!!
Lots of photos and memories.
(pastries and fresh fruit and coffee and milk for breakfast in our room, with the fresh springtime breeze and sunshine and the sounds of the streets of NYC wafting thru the window... DH, going out at dawn to get coffee, and being asked by a pimp if he 'needed a woman'... he was like, "... no.. I just need some breakfast." Hahahaha!!!)
We all enjoyed it!
I would love to go back with just DH, and have a more adult visit!
Dining, Broadway, etc...