Cheap but ok
1. Jamerican Steve
What is cheap for us may not be cheap for you. You need to specify a price range.
Stay in a private room hostel if you want to spend under US$100.00 per night.
Stay in an Inn if you want to spend under US$150.00 per night.
Stay in a NJ Hotel if you want to spend under US$200.00 per night.
Stay in a NY Hotel away from Manhattan for under US$250.00 per night.
Try using priceline.com. I have used a bidding strategy to continuosly get 4 or 5 start hotels up to 50% off in New York City. There is a strategy to maximize your rebids and get the best price.
Hostels for example. Or, you can find a list of hotels in a particular area and choose the cheapest.
the colonial house inn
look it up, its a cute town house in chelsea, nyc, i was going to stay there for 2 days but had to cancel, very affordable too
the Y has residential rooms
6. MAIL BOX
Good luck with that!