I’ve now been living in NY (in the Bronx) for about 6 months. Here are some things I’ve learned by experience:
Keep in mind that transit times can be enormous in the NY area. Commuting times aren’t really considered “long” unless they’re greater than an hour and a half. This means that, in general, NYers have a much higher tolerance for spending forever getting from one place to another. People who tell you that “it doesn’t take very long” to get someplace, or that it’s a “quick trip” from one place to another might mean that it’ll take you an hour on a subway, not including any delays for work on the tracks (there’s always some part of the track being repaired, and it slows down the trains) or other service changes.
If I were you, I would plan my sightseeing borough by borough (or neighborhood by neighborhood), so you don’t spend a ton of time in transit among the things you want to see. It would probably make sense to plan your routes with hopstop (www.hopstop.com) the night before you plan to go wherever you’d like to go. Try to see things in clusters of places within walking distance from each other. Because you’ll be in Manhattan, the subways and buses will probably be pretty reliable and arrive more or less on schedule. Some subway trips between points of interest to you can take under half an hour. In other boroughs, especially ones with smaller tax bases (like the Bronx, which, IIRC, is still the poorest of the boroughs), transit can take much longer than you’d expect.
Be prepared to feel exhausted by mass transit, especially the subway. The subways can be really filthy and unpleasant at times. They’re often the most convenient way to get between neighborhoods in Manhattan a lot of the time, though, so they’re often worth putting up with. The Manhattan buses aren’t bad, though, and the commuter rail is actually pretty nice. Express buses can also be pleasant, with plush seats and smooth rides.
Each borough is a city unto itself. Don’t necessarily expect the same conventions to hold in Manhattan as in Queens or the Bronx. For example, the cute yellow cabs you see on Sex in the City are common only in Manhattan. The other boroughs have big black cars with diamond stickers in the windows. Most tourists breeze in, check out specific, very famous things in Manhattan, and then take off. There are lots of places in the outer boroughs that are more than worth your time to see.
In winter, it gets very cold outside here, so people try to compensate by making it very warm inside. I’d suggest dressing in layers, with a thick winter coat on the outside, so that you can be well bundled up while you’re on the street, but you can be comfortable in the artificial summer once you get to where you’re going.
Oh, and, for whatever reason, NY can really dry you out. I learned to carry water with me everywhere, especially when I’m traveling between boroughs or for long distances within Manhattan.
As far as the cultural niceties here in NY–really, there aren’t that many. The big ones are: 1) Stay the hell out of the way of traffic. Let people getting off trains and buses get out quickly. You dont’ enter until the last person is off. Don’t stand in the middle of hallways. 2) If someone pushes you or does something else that seems aggressive, brush it off and stand aside for that person. It’s not worth getting into an argument or fight over. 3) Don’t make any eye contact with crazy people. When you’re in mass transit, don’t make eye contact with anyone you don’t want to say something to. 4) When asking questions on the street, or when asking for basic info, distill everything you want to say down to the very shortest, quickest, and clearest version of whatever you want to get across. There will be no tolerance for spending time on niceties or chit-chat. Save your conversational skills for times when people are getting together specifically to talk or get to know each other.
Don’t worry too much about looking like a tourist or seeming moronic. The fact is, almost everyone on the street is going to be too busy to pay much attention to you, anyway. As long as you keep basic street smarts about you and don’t block traffic or gawk all the time, you should be OK.
A lot of people–me included–often feel like they’re rarely ever clean while they’re in NY. There’s this fine layer of subway grit that seems to settle on everything. You might find yourself going through changes of clothes more rapidly than you’d planned on.