I'm not from NYC but I here's some things I learned from my visit.
Get a 7 day metro card so you can ride the subway and buses free for a week ($30)
Download Google maps to your cellphone and type in your destinations and sort your results for "public transportation." That app will tell you what station to go to, what train to take and what time it departs. Also, download the "NYC subway" app cause it has a map of the NYC subways built into it. That way you can be sure, where you are when you are underground (phone data doesn't work when you are on subways) Give it 2 days and you will have mastered of the subways like a local.
Okay, now that you have the free and fast transportation anywhere in the city, it's time to reference this
http://newyorkcityskateparks.com. and that quartersnacks link (wish I would have had that during my visit)
There are plenty of places to drink in NYC at night and I highly recommend Max Fish on Sunday nights. It's not so crowded then.
People/media have taught me that the people of NYC are rude and pushy but from my experience, nothing can be farther from the truth. Be kind, respectful, positive, and don't waste anyone's time and you'll get along fine in the greatest city on earth.