The Pod is a cheap and nice place to stay. My friend stayed there recently for about $100 and gave it rave reviews. Also check out hostels, you can get private rooms and sometimes private baths. But make sure to read the reviews – there is definitely a difference in cleanliness. I recently stayed at the Candy Hostel for about $100 for a private room shared bath and it was pretty clean.

As for things to do, there are plenty of cheap or free things to do. Walk across the Brooklyn Bridge from Brooklyn to Manhatten after dark – it’s beautiful and free. Take the Staten Island Ferry for a great view for free. Search free NYC in google and you’ll get lots of suggestions.