Check this out --
http://www.touring-ohio.com/ohio-quilt-shops.html
I live on the east side of Cleveland. I've only ever been to the shop in Akron (less than a mile from my in-laws) -- nice place. The website doesn't measure up to the quality of the shop, though.
There are some more in the Cleveland area (Olmstead Falls) -- some more in the Akron-Canton area (North Canton, Canton, Copley, Wadsworth, Kent, Cuyahoga Falls) -- some northeast of Cleveland (Madison) -- some down in Amish County (Berlin, Charm). I know there are also some in the Geauga county area that are not listed, but I haven't been there.
Good luck! Let me know what you plan do to!