There are two FB groups that advertise a lot of housing and roommates so that's a great place to start, I believe one of them is 'Case Housing'.
Most grad students at CWRU live on the 'east side' in or near University Circle, there are some new modern high rises that have kind of pricey rents, but generally if you want to rent an apartment in Little Italy, Cleveland Heights, Larchmere, or Glenville (not as common but I like it), you will find extremely reasonable rates. I found housing on Craigslist a few times in the city and didn't have any issues. I would visit if at all possible as you might find that the west side is more your vibe and a lot of people like Ohio City, depending on location you won't be too far from the university as long as you're open to the red line. Hope that helps.