I've recently discovered Celina, OH and the Grand Lake St Mary's State Park, which is about 70 some miles from Findlay. I've never been there, but I've been told it's beautiful and a fun place to be. Check the Ohio State Parks website for more info on this park, or any other that may strike your fancy. I've always found State Parks are great places for exploring the outdoors. And usually the nearby towns are nice small quaint places.....quaint meaning not necessarily all built up and commercialized....which translates into "easy on the pocket book"......usually, not always.

Since I don't have a doggy, I'm not familiar with any dog friendly places, but again, small towns are usually pretty accomodating to friendly people.