We went for a week to NYC in Feb. 09, with our then 9, 6, and 3 year olds. The first thing that shocked me was just how much walking is required in the city! You are literally walking all day long, which is pretty neat, but if you're not used to it, it can be exhausting. I would highly recommend that you start now thinking about ways to do more walking around home, and bring the kids with you, or just take long walks as a family. And invest in shoes that you'll enjoy walking around in all day.
The second thing that shocked me was just how expensive it was to do *anything*. It is completely worth getting a weekly subway pass for everyone. We were only there 6 days, but the pass paid for itself within 3-4 days, especially since the best hotel rate we could find was in Brooklyn, which meant crossing a tunnel everyday to get into the "city". We loved the "slice of life" experience we had in Brooklyn, too: the local delis, just walking around and people watching. We spent 1/2 a day doing that (technically, everyone else did, I had a bum ankle, and was resting before going into the city for our show that evening).
Definitely wait to do the half-price window, but be flexible in your plans, either for which show(s) you'll see, or on which day.
If you like musicals, there's a great diner just off Broadway where local talent performs major hits from Broadway musicals, nearly constantly during the dinner. That talent is also the waitstaff. It is very interesting, very up close and personal with the actors, who are all working to get on Broadway. We ate there for several meals!
If you want to do a Statue of Liberty tour, get in line first thing in the morning. Plan on being at the ticket office 30 minutes to an hour before it opens, just to be able to be sure to get a tour that day. We did not plan ahead on this one, you may be able to purchase advance tickets online. Hubby and children spent a couple of hours in line, only to realize they were not going to be able to get on the ferry that day. They went to the Empire State Building instead, and had a great time.
Have fun!! I wish I could go again!