When I have stayed in cabins down in Hocking Hills, I have stayed with Get Away Cabins: http://www.getaway-cabins.com/
I have stayed in many of there cabins and all have been very nice and we never had a problem with any of them.
But as someone else suggested, if your heart is not already set on the Hocking Hills area, head down to Gatlinburg, TN. It is an 6-8 hour drive and there are a ton of beautiful cabins down there and some of them are even cheaper than the ones in Hocking Hills. I normal get my cabins down there from Heartland Rentals: http://www.heartlandrentals.com/