Museums in New York can be amazing. They can also be pricey (unless you know where to go to pay no admission). If someone's visiting New York, looking for some non-touristy things to do, I will always tell them to go to Chelsea on a Thursday night because they will likely love it. I first went when I was twenty and I'll still agree now that it's such a good way to spend an evening in this city,
Every Thursday night between 6pm and 9pm, there are a ridiculous amount of (free) gallery openings in Chelsea. There is such a variety of what's showcased (one place could focus on electronic media and the one next door could be purely installation) and it changes so frequently that you'll rarely see the same thing upon two visits. There's also free wine and sometimes food at all of them, since, well they want you to come. You can take a look at what's scheduled ahead of time at sites like Art Cards or Meet Up - but that isn't really necessary to do since you can just pick a street to start on and walk around from there. Most venues are between 22nd and 27th Streets (and from Seventh Avenue to Tenth Avenue), but there are definitely some more spaces (less congested) spread along the outskirts of Chelsea.