I'm in the same boat -- accepted to CU but with major housing issues.
I've been to Columbia many times (a good friend was an undergrad there) and I've visited the SPH. Let's just say that you'll want to live closer to the undergrad campus (114th & Broadway) than the SPH, School of Medicine, etc (168th). The undegrad campus is in Morningside Heights which is a pretty decent neighborhood. The SPH is in a seedier section with less commercial access and neighborhood feel.
CU, in general, is near/in Harlem. Overall, it is pretty safe (I never felt uncomfortable) and students can walk around the surrounding streets (Amsterdam and Broadway) freely. Of course the wealth of the University and its students attracts the wrong kind of people but CU is generally safe by all of my friends' accounts. It has great subway access that'll get you between the two campuses quickly. The undergrad campus is also very close to the NW corner of the park.
Columbia is one of the largest owners of property in NYC, specifically Manhattan. All of the housing my friend lived in (I saw three different buildings between the times I visited) were pretty nice for NYC standards. Almost everyone at CU lives in their housing.
What I'm not sure about are these two issues:
1) How much does it cost, especially compared to what I'd pay if I hunted on my own?
2) Can I apply to live anywhere in their housing selection (closer to the undergrad campus) or do I have to live near the health sciences complex?
I will be attending the April 11 Visitor's Day and I hope to find out there. Let me know if you hear or find out anything in the meantime.
You going to the visitor's day?