My wife and I love to travel, so we take our kids on these big trips hoping to instill in them a love of travel too. We are going to NYC this summer and my two daughters are 8 and 5. Will they remember everything? Probably not, but I think they will remember the major stuff and they are going to have a blast. We did Chicago last year--Wrigley Field, Museums, Aquarium, Sears Tower, Navy Pier, Deep Dish pizza, etc. and my daughters still talk about the trip.
When we did Chicago we used CityPass. It allows access to the top 5-6 spots in the city, and as a bonus allows you to move right to the front of lines. They have one for NYC as well:
http://www.citypass.com/new-york
All the top (touristy) stuff is included--Empire State Building, Met, Statue of Liberty, 30 Rock, 9/11 memorial, Intrepid. I think it is worth the money.
We are staying near Times Square as that will give us a good point to take the metro to the places we want to see. I found a hotel for $250 a night. We also have tickets to Yankees vs. Red Sox! Can't wait for that.
I know it's touristy but I love walking the Brooklyn Bridge, then having pizza at Grimaldi's, followed by ice cream on the pier over looking southern Manhattan and the Statue of Liberty.