Sadly NYU is a school with less emphasis on community than others. That can’t be helping to you at all. I’m sad that you’ve had this experience. Please rest assured that NYU and lower Manhattan is not representative of the rest of the East Coast. I hope that you find the sort of community that you need.
Living in NYC, I’m trying to think of other ways for you to create community for yourself while you’re still here. One of the tropes of NYC is that the first year is such a culture shock for many people that they really have a hard time. The second year it starts to get better. Often the things that shock and annoy new-comers are the very things that later energize them and make them find the city vibrant and stimulating. Manhattan really isn’t like the rest of the country. Even going uptown to quieter neighborhoods might help you find more quiet, community-based living in the City, and getting outside of the City a little might also help.
NYU and Columbia share a lot of events and cooperation. You may want to go uptown to events at Columbia/ Barnard, where it’s quieter and where there is a real neighborhood. There are also woods and trees, bird sanctuaries up that way, walks in the woods and a riverside walk. Look on the Events calendar on the columbia web page for things open to the public.
Maybe see if there are meetups that you could join. One nice thing about NYC is that there are so many people that even if you have a niche interest, you’ll find a group of people who share that interest–hiking, sci-fi, writing, food, arts, music. The city park system and library system also offer free events. They can get you out in places that you wouldn’t expect NYC to have. For example, there’s a guy who does wild foraging lectures in the parks; winter survivalist lectures; or maybe go owl watching at night in the autumn when you can see them on the bare trees.
See if you can find a groupon to do something like night kayaking on the Hudson.
If you feel the need to volunteer and don’t want to be overly organized about it, there’s a great opportunity every Saturday morning and Tuesday evening. You can help handicapped people work out. Just drop in. All handicaps are welcome; all athletic abilities welcome from walking a few blocks to sprinting marathons. The organization is called Achilles. You meet at the Engineer’s Gate in Central Park at 90th and 5th Avenue all year around and in all weather. They pair people up by what they want to do that day. The community is warm and inviting. http://www.achillesinternational.org/nyc-chapter/
If you’re religious, there are many churches and temples, many of which offer wonderful communities and outreach to the public. St John the Divine at 110th and Amsterdam has pleasant gardens with peacocks and on Sunday they offer a lovely vesper services in the afternoon. If you’re not religious, there are secular groups such as Secular Humanists.
Brooklyn has many neighborhoody neighborhoods. There’s also a thriving art scene at BogARt in Bushwick, with Roberta’s pizza nearby. On nights with openings, there’s a big party there where you can meet people and look at their art. – http://56bogartstreet.com/About.aspx