The housing thing doesn't really affect me as I grew up in the area and will probably live at home for first year...
But, for people coming from other areas... Housing depends a lot on a few quesitons:
1. Do you have a car?
2. How far are you willing to drive each morning?
3. How concerned are you with price?
Some things to keep in mind...
You may want to live close because you don't have a car... My only advice to that is GET A CAR! Seriously. You need one. Cleveland is a driver's city and public transportation is almost non-existant.
Apartments near the school (Cleveland Hts, University Hts, Shaker...) are reasonable but if you drive a little further out it can get a LOT cheaper. I have friends living in Parma and Rocky River for $400-$500 instead of the $800 to be near school. Plus if you get a $400 one-bedroom you have your own place for the same money!
If you don't mind a drive (twenty minutes to a half hour) Lakewood is probably the best Cleveland suburb for rental properties. Nearly the entire city rents rather than owns thier homes and there are many more apartment buildings than in most of the Cleveland area.
If you can get a few people together it may be worth renting a house. It can actually work out to be cheaper.
I don't know if any of this is helpful... I've lived in Cleveland my entire life (except for undergrad) and figured as I'm familiar with the city I'd offer my opinion. So if anyone has any questions related to the location, Cleveland, stuff to do... just let me know!