Fellow Mustachians, living in New York and it being summer, our apartment is booked up like a hotel with friends and family coming to visit from out of town. Tourists to NY always want to do the same things -- go to Times Square, and go up to the top of Empire State Building / Top of the Rock / One World. While Times Square is free (if you don't take pics of the 'performers') most other tourist traps are incredibly over priced. Most other activities -- eating at fancy restaurants, broadway shows, shopping, are all obviously expensive.
To that end, I've tried to come up with a list of free activities in the city, and would appreciate any additional suggestions!
Museums/Art
MOMA is free after 4 pm on Fridays
Guggenheim is free after 5:45 pm on Saturdays
Art galleries in Chelsea can be free, and sometimes will even serve wine/beer (cannot verify myself but from research)
Parks and Recreation
Picnic in Central Park (BYOB but keep it low key because it is prohibited. Pour wine in a water bottle and voila!)
New York Public Library (but the famed reading room in the library is currently closed down due to asbestos) - famous in many films including The Day After Tomorrow.
Bryant Park has free movies in the summer (very crowded though) and free yoga
NY State and Federal Court houses downtown - from every episode of Law & Order, although I believe the stairs are off-limits due to security. You could probably go in and watch any number of trials that are open to the public.
Brooklyn Botanical Garden Free on Tuesday
Socrates Sculpture Park - Free Yoga and Tai Chi
Highline is free to walk
9/11 Memorial is free to visit, but the museum and tickets to the top of the observatory are pricey (and not tasteful in the case of the museum)
Bronx Zoo is Free on Wednesday
There is only 1 free tennis court I know of - on the west side highway in Chelsea, generally with a wait of +1hr. Other tennis courts such as Central park are $20/hr.
Entertainment
Tonight Show with Jimmy Fallon / Late Show with Stephen Colbert tickets are both free if you go at the right time and wait in line. It's also free to go to the recordings of GMA and all that crap.
Brooklyn Brewery has free tours (the beers are not free, however)
Brooklyn Bridge is free to walk
Harlem Gospel Churches - lots of out of town friends have gone to the churches in Harlem as a form of entertainment, despite not being Baptists. I assume this is OK, but I would think a donation should be made.
Staten Island Ferry - is free compared to the tour boats that leave from Chelsea, and goes right by the statue of liberty.
NY Federal Reserve Bank gives free tours, has some vault full of tons of gold
The campuses of NYU (near 14th street) and Columbia (near 116th street) are both free to visit
There are dozens of famous churches and cathedrals
NB - Broadway tickets can be had for cheaper by going to the TKTS booth in times square and waiting for discounted tickets. Drawbacks are that not all shows are available, and you must pay for the best available seats (although at a steep ~40% discount). You can also go to the individual theatre that has the show you want to see and do a lottery in the AM of the day of the show.