Lived in NJ for 13 years and still haven't visited NYC. What should I see/do when I go?

Took my girlfriend to Disneyland for valentines, she loved it. She has wanted to go for 7 years but never had the chance. I've lived in NJ almost 13 years and have never taken her to NYC. Maybe I'm stupid or I just don't know how to make it? She is short on money so I plan to take her for free. We are privy to the oddities? She watched that tv show so she'll want to see the places they took her. Any ideas what to do/see and free options?<br><br>Edit: had to delete my throwaway account but I'll continue on this one. Went 2 days ago and she loved it. <br><br>We started in Chambers st subway privy to the oddities. 2 blocks? Walked up to the World trade center. My girlfriend was very moved by the memorial. She loved it a lot. We stopped in the museum for about 15 minutes. I'm actually sad we didn't go in because the little we saw was great. $32 it's ridiculous. <br><br>We took a ferry to Liberty island and Ellis island. We actually chose the least expensive option just $18.95. She loved it a lot but I did feel rushed at Ellis island. <br><br>After the ferry we walked to the bridge and walked across but almost got caught in a storm so we rushed back from DUMBO. <br><br>Till you can't take anymore! 4 days, please!