Here is a list of some really good museums of New York that I visited and enjoyed :
– MoMA (Museum of Modern Arts) : Every Friday afternoon after 4pm the admission to the museum is free. There is often a line outside the museum but it goes really fast.
– The MET (the Metropolitan Museum of Arts) & the American Museum of Natural History are both “pay as you wish” museums. Yes it means that you can pay only 1$ if you want (and if you feel comfortable enough once you’re in front of the guy selling the tickets!). And since the MET is really big and you cannot possibly see everything in one time, you will want to come back several times (it may take you a while before you get to see the entire museum…!) and it’s nice knowing that you won’t ruin yourself.
– The Whitney Museum of American Art is a great museum at the end of the High Line that will definitely give you a really good insight on American Art. Every Friday from 7pm to 10pm the admissions are pay as you wish. It can be a good idea to arrive 10 minutes before 7pm, there is usually a line and they close the access when they reach maximum capacity. If you go in January-February, you could still be able to see a super-cool sculpture of a 8-foot man made of wax (a giant candle!) which is melting little by little.
– The admissions at the Frick Collection are free each first Friday of the month from 6pm to 9pm. I highly recommend you to visit this museum for its pieces of arts but also for the building itself which is the beautiful New York city mansion. And also, they usually organize music and dance performances for first fridays at the museum. When I went there, there was a jazz concert, little toasts and drinks, and they provided material to sketch the sculptures of the Garden court. You really need to be in the line before 6pm if you want to have a chance to get in, the line can be really long and they stop the line when the max capacity of the museum is reached.
– The Neue Galerie (Museum for German and Austrian Arts) is also free on First Fridays from 6pm to 8pm. It is a museum I really want to visit but when I went there, I arrived a bit after 6pm and the line was so huge that I couldn’t get in! Sooo… be there really early!
This list is not exhaustive, and need to be completed but it is a good start (believe me, they are really great museums!). The only thing is that many people seem to agree to the fact that it’s nice being able to visit museums without paying a lot, which means that inevitably these museums are often really busy!