>>375001Dogs must be on a lease at all times in the Smokies. They aren't technically allowed in the backcountry at all. Which sucks. But I take my dog hiking off trail sometimes, where I know it's unlikely that we'll encounter anyone. Just avoid official hiking trails and the touristy parts. (cades cove, clingmans dome, gatlinburg) And walk with a leash in your hand so you can put it on your dog at a moments notice. If you do all that, you should be good.
The WMAs are good places to take your dog. At least during the off seasons.
http://www.tn.gov/twra/gis/WMA_Home.htmlhttp://www.tn.gov/twra/pdfs/wmaseasons.pdfThere are lot of places beside the Smokies that allow dogs. Most require leashes. But some just state, "You must maintain control of your dog at all times." So as long as your dog listens to you, they can run free. You'll have to research for yourself on what places allow what. But the link below is a good place to start. It's a pretty good resource to find places to go /out/. Especially if your new to the area.
http://www.outdoorknoxville.com/places 