To be honest, most of the housing in the University District is already accounted for. I would look into housing NOW if you need/want to be in the immediate off-campus area. If not, I would still start looking soon at things like Craigslist for surrounding districts (Clintonville and The Short North are both close to campus and easily accessible via bike, public transit [the fee for which you pay automatically by enrolling], and, for the Short North, by foot). We are a huge university and our housing search starts in January for leases that start in August/September.
I don't have experience with the grad housing, but I did live on campus for a year as an undergrad and figured I would speak up, since their rules are probably harder to live with than grad rules would be. That being said, we didn't really have rules. No curfew, so rule against opposite sex in your room. The only rules were no alcohol, drugs, or candles, and quiet after 9 during finals week.