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/
Helpful hints on navigating the New York subway. This beginner's guide will is a great intro to New York's subway system to help lessen your apprehension.