Okay. So. I would recommend doing those hop on hop off red bus tours first. I know its fucking touristy but it allows you to really get a feel for the layout of the city and see everything for way cheaper and easier than the subways. Do that early. Enjoy it. Don't feel like you need to stop everywhere.

The other place you must visit is a place called Cuba on Thompson and West 4th. They have the best mojitos ever. Get a pitcher if you have anyone with you. I also recommend the emenadas, ceviche, calimari for apps and ropa vieja or paella valenciana. Share everything. That's near Washington Square park so you can wander around there. There are a bunch of really divey type bars around that area. Sometimes it feels really college-y though because NYU is right there. I don't know how bad it's gotten.

There are a bunch of places that are less touristy but still give you that NYC experience. Really, NYC is about wandering around. Central Park is really nice to wander in. See if there are any street fairs or anything when you're there. (link? http://www.newyorkled.com/nyc_events_street_fairs.htm)

I would recommend seeing something on Broadway just to do it. Theres these things call TKTS booths near Time Square that sell tickets day of for cheap. Don't worry about seat or anything. Get them cheap, enjoy the experience. and don't blow your entire life savings on a show. Also, eat BEFORE you get to time square. Fuck that place for food.

Reddit has a crazy awesome NYC subreddit with tons of information too:

http://www.reddit.com/r/nyc/wiki/food

http://www.reddit.com/r/nyc/wiki/commonquestions#wiki_new_york_for_cheap

They used to do a Tuesday night meetup at Peculiar Pub. I don't know if they still do. While I normally wouldn't recommend meeting up with redditors, the NYC crowd is really diverse and fun and most are late-20/early-30s professionals, not awkward children.