Stree levels are above the river, but there's a lot of underground spaces, including train stations, as this cutaway of the future station at WTC stop (Church Street Station looking west).
...and the Atrium:
http://www.hudsoncity.net/tubes/gatewaytubepage.html ....under construiction now.
More on the Hudson Tubes page.
Interesting. Hudson Tubes is what the subway trains between New Jersey and New York were called until some time in the early 1960's when the PATH acronym was adopted. Are they going back to using the original name and dumping PATH?
BTW, if memory serves, PATH stands for Port Authority Trans Hudson.