Here’s an idea ..take advantage of the NJ Transit Light Rail system.
www.njtransit.com
You can take it from Lincoln Harbor to Hoboken, walk around Hoboken go over and buy something in the Cake Boss’ Bakery. But the lines are very long. (and no fast pass)
www.carlosbakery.com
You can also take the Light Rail to Liberty State Park. Liberty State Park is an attraction in itself. Great water walkway. On the walkway you can snap great pictures of the NYC skyline, Ellis Island, Old Jersey Transit Terminal, and SofL. As you already know you can catch the SofL ferry from there. (the picture in my sig is from Liberty State Park...pre 9/11

)
www.libertystatepark.org
I am sure you did research and you know that the NY Water Way ferry to NYC is right near your hotel. That is the one which will take you over to NYC 39th street. From there you can take free shuttle buses to different parts of NYC. We usually just walk the many blocks to Times Square.
www.nywaterway.com
Also the NYC side ferry terminal is almost right next to the USS Intrepid. Great place.
www.intrepidmuseum.org
While in Weehawken go eat at the Chart House. Great views of NYC go at night. There are also a few other nice restaurants in the area with beatiful views of NYC
www.chart-house.com (click on locations...NJ)
www.watersiderestaurantandcatering.com (right down the road from the Chart House)
PS - I just remembered you can take the NY Water Way ferry to a Yankee Game.
www.nywaterway.com/ToursYankeeClipper.aspx
Have fun!
