My friend delivered at NYU Medical Ctr and she said that they have very few private rooms so if it is a busy time, the chances of getting a private room are slim....however the hospital itself is excellent.
I got a private room at Mt Sinai pretty easily, I delivered in january. Another friend delivered at NY Presbyterian, delivered Nov 2007 and had a private room as well. NY Presbyterian is supposedly the best hospital for L&D and NICU unit. I personally loved my ob's so I went with their hospital affiliation, would def deliver there again as well so I guess go with whichever hospital your doctor is affiliated with assuming that you are happy with them.
Mount Sinai...you get private birthing rooms and the nurses and doctors are amazing!!!! the delivery wing entrance is on 5th ave and 105th street, i believe.
I had a m/c there and they couldn't have been nicer. I didn't want hospital food and they let my friend go out and bring me comfort food. I would reccommend them ANYTIME.
I am planning on St. Luke's Roosevelt after a really good recommendation from a friend.
ALL of their delivery rooms are private - but your recovery room may not be (pay extra).
I have heard that Columbia is rated number 1 - but if you have a typical pregnancy then it probably isn't the best because the staff isn't super friendly (so I've heard). I have only heard good things about St. Luke's Roosevelt. I mentioned my selection in my blog post last week, if you are interested. http://pregnantpeacock.blogspot.com/2009/05/pregnancy-week-5-first-trimester.html