Maid Service

Go to the NYS Unemployment office and find the line that has the out of work real estate brokers. I hear they do excellent apartment cleaning. They do windows and floors too. Washing the outside of windows in high rises is a specialty.

I would just ask your new neighbors who they use

Nobody I know in NY has a "maid service". Everybody I know has a "cleaning lady". Difference is that instead of hiring a big company you hire an individual. As Primer05 said, ask your neighbors. Most everybody I know loves their cleaning lady and would be happy to give you her name. You will get much better service with a cleaning lady than hiring a service.

Building doormen always know someone. If your building does not have a doorman ask the doorman in the building next door. Typical cost $65-$85 including tips for 1 bedroom depending on what you want the cleaning lady to do. For $85, they will do your laundry too (you pay for machine, and detergents etc).