Free Tickets for the American Natural History Museum
Try going there around 4:30 in the afternoon.
However, this is nothing official and not guaranteed (no official free entry program on the website), only an educated guess. My guess is because the museum closes at 5:30 and there are remaining tickets unsold, so they just send free give aways.
I found this by accident. My friend and I were taking a walk in Central Park and I was looking for a bathroom so we walked into the Museum. Luckily we got to enjoy the Museum for one hour for free. This is truly a city full of wonders!

American Museum of Natural History
New York