The great thing about New York City is that there is a tremendous number of things to do that are free. I have lived in New Jersey for my entire life and no-matter how many times you go to New York they never get boring.
Below are some of my favorite attractions, You need to remember this is like a walking tour of New York so you need have comfortable walking shoes, water and and time.
Usually I start off at Ground Zero - the site of the 9/11 Terrorist attack. Although this is a solemn site, many people come to the site to reflect on the tragedy that happened at that location.
From the 9/11 site, proceed toward the Hudson River over to the World Financial Center. Inside the glass domed atrium you will find marble stairs and palm trees in the heart of Manhattan. Exit the World Financial Center and head toward the River. Notice the large yachts docked right out outside of the center in the marina.
Take a stroll from the Marina toward Battery Park along the Promenade and enjoy the views of Jersey City Waterfront and distant views of Ellis Island and the Statue of Liberty.
Once you reach Battery Park, here you will find street performers, vendors and musicians. If you wish to go to the Status of Liberty or Ellis Island - you can catch a ferry from Battery Park (Admission is required for the ferry, Statue and Ellis Island).
Brooklyn Bridge - Manhattan - Attraction - Cruise Passengers
For free views of Ellis Island, the Status of Liberty, the Manhattan Skyline and the Veranzarro Bridge - I recommend taking the Staten Island Ferry. The ferry ride is 60 minutes round trip from Battery Park, Manhattan to St. George Staten Island. The view of lower Manhattan from the ferry is outstanding and the ferry is FREE. (Please note that you will have to disembark from the ferry when reaching Staten Island, just exit the ferry and re-board). If you are taking a cruise departing from Manhattan I would skip the ferry ride, since the views will be the same as when your cruise departs.
After the ferry ride, you can proceed to the South Street Seaport and see the historic sailing ships moored at the location. You can also enter the indoor mall. I recommend going to the upper balcony of the mall to take photographs of the Brooklyn Bridge. After departing from the mall cross the street and visit the cobblestone lined street and additional stores of the Seaport.