It does depend if you are going to NYU or Columbia... if it is NYU, you could live in Brooklyn or Queens... there are safe, nice neighborhoods in those boroughs with great transportation that would get you to class quickly. I know a lot of NYU dental students live in Stuyvesant Town, which is in Manhattan but has a few parks scattered throughout the apartments, so you could easily take a walk or run and feel like you are in the park. For Columbia, you could live in Riverdale which is a very nice part of the Bronx (my sister lives there.)
What exactly don't you like about the city? There are parts of Manhattan that you wouldn't feel like you are in the city that much...places like Battery Park downtown is close enough to everything but has parks, and it's on the water...
does this help?