Getting into a New York State of Mind

So, I'm headed up to NYC on Wednesday night.

I can't get crazy spending money because I'm taking this trip without any pay coming in, but I do have ALL of Thursday footloose and fancy free with all of the time from breakfast to after dinner getting from Bronx-ish to Brooklyn. So I'm looking for recommendations on:

1) Cheap/free things to do or see

2) Cheap, good places to eat

.... and because my hair is making me crazy

3) a good, reasonably priced walk-in place for a haircut