When I stayed in NYC I stayed at the Leo House in Mid-town Manhattan and it was great. It's a Catholic retreat house that's more like a hotel for males. You get your own small room and have to share the bathroom like you would at a university. Very low rates. I don't know if you're Catholic, but I'm not sure if that's a requirement.
http://www.leohousenyc.com/index.php?option=com_content&view=article&id=49&Itemid=55There's also AirBnB:
https://www.airbnb.com/s/Manhattan--New-York?af=1922719&c=A_TC%3Dnkjf82rd4h%26G_MT%3Db%26G_CR%3D83286410522%26G_N%3Dg%26G_K%3D%2Bguest%20%2Bhouses%20%2Bmanhattan%26G_P%3D%26G_D%3Dc&pg_tb=47.21&gclid=Cj0KEQiA1dWyBRDqiJye6LjkhfIBEiQAw06ITvxDS34zttDaAV_5K4t0RXCMrqtSuo8xhv1gNb2aV1saAnqj8P8HAQ
Oh yeah, I agree with the other posters recommending Southwest Airlines. They're pretty friendly and have decent prices.
