Know the lines and stops: New York City Subway Map. $2.50 per ride or If you’re buying more than 13 individual Metro fares on your trip, buy a 7 day unlimited pass for $30
NYC subway in the bad old 1970's - and my sister and brother and I rode it everyday from the Bronx to school on the upper west side.
An MTA MetroCard can be used for both subways and buses, and transfers between the two modes of transport - which run 24 hours a day - are free. Accommodation in NYC: http://www.roomyeti.com/rentals/united-states/new-york/new-york/