Apart from all the fab hotels mentioned, there's also another way if you want to stay in NY:
http://www.homeaway.com/.
I waited to post a reply until I mentioned this thread to my wife.
My wife used to travel a lot to NY for her work up to few years ago. Sort of 1x every 3 to 5 weeks for a 4-5 days stay. She always stayed at the Gansevoort:
http://www.hotelgansevoort.com/ but that was paid by her company. She runs her own business now and she visits NY on a 'once every six months' basis. She not longer stays in the Gansevoort, but uses Homeaway.com for a nice place to stay. Often a small appartment or a loft, sometimes a larger appartment etc.
If you want a list of nice places to visit, just drop me a PM, I will ask my wife for an answer. And there's a nice iPhone app for your travel plans:
http://www.worldmate.com/iphone/
About flying: flights out of NY to Europe on Friday tend to be more expensive than flights on Saturday. Often, it's even cheaper to stay in the hotel/appartment for an extra night and fly out on Saturday!
Menno