Greenwich Village (more often known as The Village, sometimes in conjunction with the East and West Villages) is NYU's neighborhood. At times more upscale and at times more seedy than Morningside Heights, it is acknowledged by all to be much more fun. If your stash is running low, Washington Square Park is a good place to start.
Originally, Greenwich Village was an area where local artists lived and worked. Due to their presence, the neighborhood because popularized and was considered "hip". Ironically enough, this let to the eviction of most true artists (gentrification at its finest).