This is your 1st trip to NY, yet no hotel booked, well, one admires you for your bravery.
This is a great search engine:
http://www.sidestep.com/hotels
One thing, if you see: Woogo Lincoln Centre Apartments give them a miss, I have no personal experience, but aware of a site dedicated to these apartments.
We have visited NY 7 times, and will be returning again in 5 weeks.
I'm sure you will receive all the assistance you require from this site, however, if I can assist you any further don't hesitate to ask.
Driver02