Yeah, Ohio is part of Appalachia (the southern part of it is) and Middleton Ohio is not part of that, although its closer to it. I grew up in the Lake Erie region so also not part of Appalachia. Also Middleton isn't all that small. Its a suburb.
I have a friend who grew up in a tiny, lone streetlight town, called Pomeroy, right on the Southern border. Basically in the foothills. That is what we mean by small town.