New York City has the best public transportation system in the world, as well as the best subway system in the world (I didn't say cleanest).
Navigating sometimes can be tricky, but using the subway is the
cheapest, quickest, and most convenient way to get around town. You can
pick up a subway map
at any subway station, and they're pretty easy to read, as long as you
know where you are and where you're going. You'll also see the most
interesting cross section of people while you're riding.
One of the particular things to look out for, though, is the difference between a "local line" and "express service" line. For example, if you're on the 1, 2, 3 subway line (which is red)
the 1 train will stop at every station on it's route. A 2 or 3 train
in those stations are express, which means they only stop at a few
stops along the way. The map will have a key with special colored dots
explaining which trains stop where. Don't let this intimidate you! If all else fails, hop on the local train; you're bound to end up where you need to be without missing your stop.
Riding the subway is the cheapest way to get around the city.
MetroCards can be bought at bottom of the stairs in stations, and you
can put any amount on them that you'd like. The MTA has a breakdown of
the costs on their website, including special bonuses if you put a certain amount on your card. You can also buy day, week, and monthly passes, for $8.25,
$27.00, and $89.00, respectively. You can save a ton by buying a pass
for your entire stay, and it will be just one less thing you have to
worry about while you're there. *EDIT: The MTA has discontinued the One-Day unlimited passes!*
Another option is the infamous NYC yellow taxi.
There are many reasons to be afraid of the taxis, but many, many more
reasons not to be. Don't be afraid of them safety-wise, those guys know
how to drive in New York City. I can understand the fear of their
driving, because they cut across 3 lanes of traffic in point five
seconds, cut people off, run yellow lights at the last second, go from 0
to 50 faster than you imagined possible, slam on breaks, turn corners
at full speed, nearly hit every car they're trying to inch their way
around, and scream obscenities in 15 different languages; but don't be afraid. Just keep your eyes on the buildings, people, and the little TV screen in the back of the driver's seat. Watching the way the driver is driving will do nothing but make you panic, so just don't do it. If they were dangerous drivers they wouldn't have the job they have.
I suggest everyone take at least one taxi ride while they're in NYC.
After all, when you're in the subway you can't see what's above
ground. Fares are $2.50 the minute you get in, and increase by .40 cent
increments depending on distance or time. Click here to learn the different increments for taxis. I would definitely save that one ride for a time when you think it's worth it;
to drop you and your friends off at a nice restaurant when you're all
dressed up, to get you somewhere that you can't find on your map
yourself, or when you've had too much to drink and aren't incredibly
sure of your navigation abilities for the subway.
Some things to remember when you're in a taxi:
The drivers know most popular restaurants, tourist landmarks, and
other well known areas, but they may need more specific information to
find that dive bar a local told you about. Your best bet is to just
shout out a close-by landmark, or a corner near your destination, and
walk the rest of the way. "5th and 72nd, please!" DO NOT for the love of all things ask your cab driver to take you on a late-night drive around Times Square (or at any other time, for that matter.)
You will just end up stuck in terrible traffic, and instead of
enjoying the views, you will be in terror at how many pedestrians your
driver almost hits. Times Square is mostly closed to traffic now so
that tourists can walk around and explore safely; only a couple of major
streets are open to vehicular traffic. (Walking through Times Square is the only way you should do it anyways, and I'll cover that later.)
Actually, speaking of Times Square; at every street corner you will approach someone with a rickshaw (or pedicab.) Whatever you do, do not let them trick you into a ride through Times Square in their bicycle basket. You will pay a terribly high fare (about $25 for very few blocks), and will sit in car and pedestrian traffic more than move. Not to mention all of the taxis that will almost hit you.