Within the city, the app HopStop is essential. Plug in your destination, hit go and within seconds it will give you the walking distance, which subways to use or how much a cab would cost. It really is a great app and I want to personally thank the person who created it. It has saved me from walking miles and miles in parts of the city that were unfamiliar to me.
While living in NYC I have traveled home, which is just an easy 3 hour bus ride, to Atlantic City, to Boston, Cape Cod and Long Island. All relatively easy to get to from New York. Having both Penn Station and Port Authority bus terminal within easy walking distance from my apartment has been both a blessing and a burden. While it has saved me from missing the bus/train numerous times, it has also caused my stress when walking to the subway in the mornings. In addition to this, two airports are just a subway ride away.
Overall, NYC is a great place for public transportations. In Manhattan, subway stops are everywhere and other destinations are within reach.