When visiting New York City, visit the outlying parts- Brooklyn, Bronx, etc. It's VERY different from Manhattan. It's easy to tell what ethnic groups live on what blocks. It's just interesting to see so many different cultures living in one city- and they all live in their own little world.
Don't be afraid to take the subway. YEah, it can be kinda confusing but don't disregard it because it could be dangerous. It is very safe now (but still smelly) and it will take you all over NYC. Just use your common sense and don't travel too late at night. Also feel free to look at the map, even NYers do it once awhile.
Subway Culture When you visit New York, something you can't miss is the pictures inside the subway stations. They are really so precious art!
New York is a working City, rather than a place designed for tourists, you may find people rude when they are only in a hurry. Avoid rush hour, and ask questions in as succinct a manner as possible. the answer may be short but the info will be good.
If anyone tries to sell you a swipe at the sub-way turnstile, simply say no thank you. They are just trying to get your money. This is illegal. Decline, and move along.
In NYC, most people on the street or subway are walking so fast, everybody looks like they are SO BUSY... So, fast your steps, stay out of others' way!:P