Yep, Ontario!   ;D  

I'm from central Ohio & I love living where I do, but truthfully, I have a hard time getting very excited about canoeing Ohio after spending time in any part of northern Ontario, esp. Quetico!

That said, I have canoed & camped in spots for a weekend in Ohio.  You can do this on the Mohican, Hocking and Big Darby.  Usually it's just camping at the canoe livery or a park & arranging pickup downriver, or drop off upriver.  

There's not a lot of public land where you'd actually canoe & take your gear with you (to my knowledge).

Any fellow Buckeyes have more useful info?
-Tom