In these maps of Greenwich Village in the 1980s and in the 2010 census, it can be seen that the percentage of young people living in the village has gone down considerably since the 1980s. This is probably due to increased rent and cost of living, and in the 2010 census, most of the 18-19 year olds can be seen centered around NYU.
Maps from Social Explorer 2010 and 1980.
