Your post made me curious to do a search online and see what I could find. I didn't find any places that sell zines, but I did find an infoshop that has a zine library: http://www.thefirebrand.org/infoshop
I live south of Nashville. I haven't heard anything from the guys who were doing the Firebrand infoshop in a while; not sure if they are still open. As for stores... not really. You might be able to find a few zines at Grimeys (a really good local record store, www.grimeys.com) but that's the only place I can think of. However, there are a couple of libraries with zine collections -- Linebaugh Library in Murfreesboro (www.linebaugh.org) and Watkins College of Art & Design in Nashville (www.watkins.edu).