Depends on what you mean by "near". I'm a member at Tusco Rifle Club, which is in Midvale http://www.tuscorifle.org/
- members only, though members can bring a guest
Then there is Canton McKinley Rifle & Pistol Club - http://www.cantonmckinleyriflepistol.org/
- members only as well, never shot there but supposed to be a nice range
And a public range in the Harrison State Forest near Cadiz - http://ohiodnr.com/Portals/18/forests/pdf/harrisonsf_map.pdf
- last time I went there a few years back there were 3 or 4 un-covered shootiing positions, 100 yard range, and when the hunters are getting sighted in it gets pretty busy...
And of course there are a few more, see http://www.muck-boy.com/Shooting%20Ranges/Muckboy%20Ohio%20Shooting%20Range%20Page.htm
but I don't know much about any of the rest.