I grew up in CT, so I'm not a native New Yorker but I've spent an awful lot of time there.
Vegan food is easier to find than you'd think. Definitely check out the raw food restaurant Pure Food and Wine (
http://purefoodandwine.com/). I constantly hear about the vegan cupcake bakery Babycakes (
Babycakes NYC™ : Bakery & Mail Order) but haven't tried it myself.
Subway, subway, subway. Cabs are okay for late-night rides home from the bar, but otherwise it's much faster to take the subway around. There are seven-day unlimited Metrocard passes you can buy (
MTA Home Page) for $24/each that will cover your stay. Of course walking beats all but I certainly wouldn't walk from Midtown to Flushing or anything like that.
Check out Strand, the used bookstore, which used to be one of my favorites before I discovered Powell's in Portland. Still a good place to find hard-to-find books.
My main advice is just to wander. That's where you find the most interesting places to eat / things to see /etc. (The MOMA is worth checking out, though.)