Cape Liberty is located at The Peninsula at Bayonne Harbor, a 430-acre man-made peninsula across the Hudson from Manhattan. To start with, Royal Caribbean will make use of existing structures but has committed to a long-term development plan that will result in construction of a new terminal.
Location-wise, the port itself is only about 15 minutes from Newark's Liberty Airport (hint: if you're flying in, try to arrange for flights to Newark rather than New York's LaGuardia or JFK Airports). Royal Caribbean is working on ferry service from Manhattan though no concrete plans have been announced.
Passengers bound for Voyager of the Seas and Nordic Empress will enjoy splendid views of the Manhattan skyline and the Statue of Liberty from land. But it should be noted that Cape Liberty is actually centered below the tip of Manhattan -- so, sailing away, travelers can certainly view those icons but they won’t passing directly by them.
Celebrity Cruises, Royal Caribbean's sister cruise line, will continue to operate out of Manhattan's port facility.