Your public library would be the best place to start. But census records will be of no use to you if you can't pinpoint where your ancestor was living in any particular census year.
You at least know where your mother was born, so that's a start. The U.S. Federal Census is taken every ten years, in years ending in the number "0". pick the year closest to your mother's youngest age (provided you're certain she was still living in Ohio in that year), and you'll have your starting point.
-- Nanaea