I would agree with KSUViolet that OSU has a thriving sorority community.
I attended Michigan State, which has a lot of similarities to OSU in terms of undergraduate population. (Greek Life actually seems to be more prevalent at OSU than at MSU.) I also currently reside in Ohio and serve as a chapter advisor at BGSU. Have heard nothing but positive things about OSU's Greek system. My first cousin just completed her freshman year at OSU, and I'm encouraging her to participate in recruitment this fall.
Do you presently reside in Ohio? If your daughter is looking to obtain letters of recommendation (I don't believe they are an absolute requirement at OSU, but they never hurt), there are several active Alumnae Panhellenics in Ohio. I believe the Cleveland area is the largest, but there's also an organized group in the Toledo area. Not sure about Cincy.
Regarding your comment about making a big university a little smaller...I absolutely agree. I joined my chapter as a freshman, and it helped to make a huge university a lot less overwhelming! (Going from a small town of 3,000 to a huge university of 40,000+ undergraduate students was like a big culture shock...my sorority definitely gave me a "home away from home" on campus, and yet I still had the opportunity to explore everything else that the university had to offer.)