Editing New York City (section)

=== Mass transit once in the city ===
New York City arguably has the best developed and easiest public transportation system of all major cities in the United States (http://www.mta.info). It is easily navigable, runs 24 hours a day, 7 days a week, and is safe. It is an aged system, though, and some subway stations can smell bad and be unbearably hot in the summer, and there is a lot of rat poison applied on a regular basis. But the subway cars are generally clean, climate-controlled and well-maintained. Also, note that you are also subject to random "bag checks" by the police at all times (but I've only seen a couple of instances of this in the last few years). 
As a traveler without a car or bicycle you will heavily rely on NYC's public transportation system and you could wind up taking at least half a dozen rides in the subway/bus on any given day. At $2.25 per ride that can become an expensive proposition. Thus, your best bet is to buy an "Unlimited" Metrocard that provides unlimited rides within on the subway and bus system of NYC (all 5 boroughs) for either 7 days ($29) or 30 days ($104). The 1-day and 14-day unlimited cards have been eliminated. In one of the most expensive cities in the world, the Unlimited ride option is one of the most cost-efficient purchases you can make. To determine if the 7-day card is a good value for you, consider this: if you pay for each ride 13 times, you have already spent more than $29. 
The Metrocards are available at all times from the vending machines in most subway stations. The pay-per-ride Metrocard will give you a 7% bonus for a purchase of $10 or more (e.g., $10 gets you $10.70). When using a Metrocard (but not the white single-fare cards), you may transfer free from local bus-to-subway, subway-to-local bus or local bus-to-local bus within two hours of the time you paid your fare. So, you could take the subway uptown and then hop on a bus back downtown for $2.25 if you get on the bus within 2 hours of entering the subway station.
Again, if you're going to spend a lot of time in the city and/or will be making a lot of trips, then you should buy the unlimited ride Metrocard rather than the pay-per-ride Metrocard.