Staten Island Ferry is free and cruises right past the Statue of Liberty - grab a beer on the boat
Go to a Broadway show and buy a half price ticket from the booth in Time Square - its worth the time spent
Buy some candied nuts from one of the vendors lining the streets
Check out whats hot from the street food vendors
A trip to Milk Bar for sweets
We loved the American Indian museum which is right by Wall St
9/11 Memorial of course
Drink on top of one of the many roof top bars one evening
https://fornino.com/locations/brooklyn-bridge-park.html
Lots of things to do in Central park
Eat a Nathans dog at Coney Island and take in the Sideshow
Gray's Papaya or Papaya King
Stroll through China Town - stop by Xi'an Famous Foods for some spicy lamb noodles
Russ & Daughters for some fish