Window Washing

I think you're going to have a hard time finding a window washer willing to do just *your* windows. It's a major undertaking that involves ladders and possibly scaffolding to conform with city codes. Most window washers bid on entire buildings.

Second video to see how it's done; first video to see NYCMatt when he was a young man:
http://blogs.todayonline.com/videosoftheday/2012/04/13/paneful-business/

Alternatively, if you have replacement windows that don't tilt in, they almost certainly unclip for removal (top and bottom sash), and can then be placed on towels in your bathtub for cleaning.

I haven't used this or any other window company, but a quick internets search yields a few places like this, at $11 per window (surcharged for excessive filth):
http://skywaywindows.com/prices.html

I see this guy in my neighborhood all the time, though I never used him. I think that he'll do one apartment at a time. http://tonyswindowcleaning.com/index.html

They used to be able to wash from the outside, with no scaffolding, by hooking their safety belt to thingies on each side of the external window frame. They're like little cleats.

It might still be allowable, as I've seen the same cleats in new construction, but on the inside. E.g., http://img.streeteasy.com/nyc/image/62/31182662.jpg, where the fixed middle pane of the window has the cleats on either side.

Id you're still looking, I can recommend Apple Window Cleaning. They charged me $70 for four windows on the fourth floor (and, yes, they climbed outside with safety belts): 212 620 0708.