For 2 years I live in NJ on weekends and rented an apartment in Manhatten on weekdays. I was a teacher in NYC. I have also traveled to NYC several times.
Hotels in the NYC area are really expensive. My advice to you would be to keep checking travel websites like travelocity (my preferred) expedia, orbitz. Check for areas around NYC like Orange NJ. The last time I went I stayed in Orange really close to the train. I walked to the train station from the hotel (less than a 5 minute walk) and just took the train in. Since you have three children it might be more cost effective to stay at a super 8 in Brooklyn because then you don't have to spend so much on the train.
Don't be afraid to stay in Brooklyn or Queens...just make sure that you're hotel is reasonably close to a subway station. That way you can easily get around.
Also, each state puts out a coupon book called room saver that has deals on hotels. They have a website as well so you could look up the deals in advance. I stayed in a hotel on the NJ side just outside the Holland Tunnel for about $70/night which was quite reasonable considering I was a 5 minute drive from the city!
Anyways, good luck and have fun! I love NY!