congrats to all accepted, Columbia is NOT in a bad neighborhood. Smelly, yes.. But it has very low crime and great restaurants popping up everywhere. NYU is much more dangerous contrary to common misconception.
So.. within walking distance of Campus
Anteka and Draft House on Broadway have some of the best pizza new york has to offer (but Anteka's deserts aren't good, go across the street to Carrot Top for amazing cannoli, among other things)
ROKC has incredible drinks, ramen and oysters. very authentic Japanese
Burger Heights (I think it's better or as good as Shake Shack), Highly Recommend Dulce de Leche Shake
A little further:
-Bodega Pizza
-Dinosaur BBQ
-The Grange
Be sure to Explore Inwood's indescribably beautiful parks. There's really no need to travel far, Washington Heights and Inwood are by far the coolest neighborhoods in NYC.