Tom, A couple of years ago we stayed at Liberty Harbor RV Park in Jersey City. from there we walked to the Grove st Path Station (on Columbus Dr). The Path subway has to lines: one goes to the World Trade Center (also near wall St) and the other ends at about 34th St and Sixth, From there you can either jump on the NYC Subway or walk. We walked for there to Time Square (discount theater tickets) and even to Central park.
Right at the Grove St Path station is a Residence Inn by Marriott (about $160). Near the next stop further west, Journal Square, there is a Ramada (I cannot tell you about the neighbor near Journal Sq).
Also from the Marriott you can walk south the Liberty Harbor and catch the ferry to Wall Street or go a few blocks eat and catch a short ferry to Liberty Park and from there you get the ferry to the Statue of Liberty and Ellis Island.
You can probably stay cheaper further out and take a train, but the train schedules are limited and I think more expensive than the subway. But you should check parking at the Marriott as it may cost. there is another cheaper hotel (other than the Ramada) near the Journal st Station. There are also hotels in jersey City near the Hudson. There is also a line of the Path that ends in Hoboken. Look up the Path map and check hotels hear the Path [font=verdana, arial, helvetica, sans-serif]stations.[/font]
All by years for traveling to NYC I hated the city, but on this trip I really enjoyed the city and going to a few plays. At the Path station you can buy a refillable card that is good on the Path and NYC subways.
Have fun.