It's a perfectly safe area, very expensive and populated by Columbia students and other sorts of rich people. Comedian George Carlin used to call Morningside Heights by another more mocking name, 'white Harlem.' If you know the cross street and avenue (for example, 112th Street, 8th Avenue) I could probably be more specific but really, there's nothing dangerous there nor should Harlem's reputation scare you.
Also, be careful with the apartment you choose, there are scams out there.