Safest area for a student going to Columbia? Willing to commute a half hour

In case I don't get housing at Columbia, I'm seeking out other potential apartments just in case. Where is a safe area for a single woman that is relatively near Columbia University? I am willing to commute 20-30 minutes (as long as I don't have to walk through any sketchy neighborhoods to get to my destination) by train or subway. I am primarily interested in family-friendly areas, so I can feel more safe.