Airbnb / apartments 
Airbnb is great to stay in New York City if you travel on a budget. You can also choose a luxurious and more expensive Airbnb, you can even stay in an entire house if you like. There are hunderds of possiblities and there is a varied availability continuously, from beautiful and spacious penthouses and cheaper smaller sized rooms, you name it. I advice you to check reviews thoroughly to make sure the place is safe and fulfills  quality that is promised beforehand. 

B&B
Staying in a B&B is also an option but not always a cheaper one. In general a decent B&B will cost between $100-$200 a night. There are several B&B's available. A B&B gives you the opportunity to discover New York City in a different way.  B&B's are located in the different boroughs including Manhattan. A unique B&B that you should definitly check out is the Urban Cowboy B&B in Brooklyn.