I spent the last 2 years in school in White Plains which is only a 30 minute train ride into the city so I was in the city pretty often. First rule, either make sure you have pants/shorts on tight enough where you can notice if your wallet is in your back pocket or put your wallet in your front pocket. Dont put your hands on the railings in the subway. Subway is convenient enough to commute around the city and much cheaper than a cab. Its very easy to navigate. Street numbers increase as you go north in the city except if you are in the financial district, numbered streets run east to west.. Avenues are what run north to south.
If you have any particular food that interests you let me know. You can PM me. When everyone is drunk there is the famous Halal food cart on 53rd and 6th. There is also a very very good halal place in lower east. Anywhere around Times Square is going be expensive for food and drink. Any person that knows the city stays far far away from Times Square. Its a tourist pit and an absolute nightmare. There are good places to eat relatively inexpensive in Midtown west closer to Hell's Kitchen. Union Square is also a fun little area for food and drink. There are also some good places to eat and drink that arent expensive in lower east. Lower east is more of a dive bar feel area. Lower west is more the bar/club scene. After 90th street its mostly residential. The other boroughs are also mostly residential as well. There are some stuff to do in Brooklyn but not much. I actually prefer Battery Park over Central Park.
You can find a pizza shop on almost any street corner as well and almost all convenience stores have a deli. Most food places stay open until 4 am. Clubs and most bars stay open until 3 AM on the weekends (Th-S). Biergarden is very good its a traditional German beer place. The big one is in Lower west.
Contrary to what was mentioned above, I thought the sex museum sucked. Was forced to go as the girls with me wanted to go. It was terrible, waste of money.
The 9/11 museum is open now and Freedom Tower is almost done.
That is a blurb I could think of at the top of my head. Feel free to PM with more specific questions.