There's probably more things to do for free in New York City than anywhere else in the world. NYC's own tourism web site compiles a "best of free" list that is regularly updated: http://www.nycgo.com/free/
This list of 40 Free Things To Do In NYC leaves out the fact that admission to the *Metropolitan Museum of Art* is a suggestion donation, or "pay what you want," as are many of the City's arts museums: http://www.lonelyplanet.com/usa/travel-tips-and-articles/76493
Everyone from the National Geographic, which has this list of some of the best free things to do in NYC: http://travel.nationalgeographic.com/travel/city-guides/free-new-york-city-traveler/ -- to the Disney-owned site Babble, has a list of free things to do in the world's greatest city: http://www.babble.com/travel/25-free-things-to-do-in-new-york-city/#25-museums-attractions-in-new-york-that-wont-cost-a-dime
And those who have the pleasure of visiting this great global treasure during the holidays will find an even greater something special in their stockings, with yet another free list of things to do: 25 Free Ways to Get Into the Holiday Spirit in NYC: http://www.complex.com/pop-culture/2014/12/25-free-ways-to-get-into-the-holiday-spirit-in-new-york-city/
In short, there's no shortage of things to do in NYC for free -- so much so that even Buzzfeed has a popular list that they have trouble maintaining due to the overwhelming amount of free things that one can do in this great city: http://www.buzzfeed.com/emmyf/free-stuff-to-do-every-day-in-nyc#.bjDERvPwdp
Finally, Time Out New York, the quintessential guide to NYC, offers this on-going list of free things to do in the world's capital: http://www.timeout.com/newyork/things-to-do/free-things-to-do-today -- which branches off into other articles containing a "best things to do for free today" and "best things to do for free this week," among other guides for the frugal New Yorker.
