On occassion, there is a party at City, and invites are usually sent through Facebook. They're usually not fancy parties with classical music and champagne; they typically focus on Latin American and African music. Only students are allowed to attend these parties, and it can be a little reclusive since it isn't open to the public. Alcohol is never served, but sometimes food is available for free. The atmosphere of these parties all depends on the host, the crowd, the music, and so on. Obviously these aren't crazy parties, and if that's what you're looking for, then New York City is the dance floor. Webster Hall is one of the biggest night clubs to head to in the city.
Keep in mind though, since New York City never really sleeps, nightlife can be more than going to clubs and parties. There are tons of other fun things to do, like watching comedy acts at clubs like the New York Comedy Club or the Gotham Comedy Club. Broadway shows run late into the night as well. So for the non-clubbers, there's always an incredible amount of things to do.