NYC is VERY expensive. Expect to pay around $400/$500 per night. You could try bidding on an online site, but be careful. I bid on a 4-5 star hotel near the American Girl store and got a great price, however... it was at the W hotel on Lexington Ave. We showed up with our 2 girls and the room was the size of a standard cruise ship room - probably, 125 sqft. Yes, one queen bed and a bathroom. Not too much room on the floor. Thankfully we brought a blow up kiddie bed for DD (who was around 7 at the time) and little DD slept with us in the bed. It was OK for just one night, but I would have gladly paid double for a larger room if we had to stay a second night.
You could try staying in some of the areas outside of Times Square/Theatre District. The Financial District, etc. might be cheaper.