Ohio quarries I've been in:
Gilboa (best viz, coldest, set up really well for all kinds of diving, great new owners).
White Star (probably second best on the viz, second coldest probably, fills, etc. available on weekends).
Todd's Scuba Circleville Twin Quarries -- small, shallow, and water gets pretty green in July\August, but a really fun place and put together really well for diving. A shop that is usually open weekend mornings.
Lakeview RV (Lancaster Ohio) -- more in there than you would think at first glance (getting out to the old two-seater plane makes for a good dive). Available for diving, but no "dive" facilities there. (Don't plan on getting fills, etc. there.)
Northpoint Quarry (Newark, Ohio) -- somebody did a lot of work to set this place up for diving, so good in that sense. Viz is not good. Would like to get there again sometime. (No fills available.)
Sugar Grove quarry -- only available for diving with Scuba Unlimited out of Cincinnati. (I think they are allowed to do training there.)
Other Ohio dive sites that I have not tried:
Natural Springs (New Paris, on Indiana Border)
Nelson Ledges (Northeast Ohio).
If you're near Cincinnati, Pennyroyal in Kentucky maybe within striking distance.
Just some thoughts. Have had fun at all the mentioned places, and Ohio divers seem to be a good community of people generally. Be ready for really cold water outside of July\August -- or anytime you go deeper than about 25 feet.