It's cloud cover that will be the question. The general Nashville area is predicted by the national renewable energy lab to have 50-60% cloud cover on Aug. 21. Below is a link to far more detail than you likely want, but it's a report they just released on predicted skies for that day across the nation. It has a map in it that gives you a good look. I intend to be watching weather forecasts closely a couple days out before I start really knowing where I'll go. I'm figuring it's pretty likely that I'll be able to find clear skies somewhere on the center totality line within an hour or two of Nashville. Nashville isn't on the center, Gallatin and other places are. So as for traffic, presumably people will be heading out of Nashville toward the center line. I am staying outside of Nashville proper so hope to avoid it that day.

http://www.nrel.gov/docs/fy17osti/68885.pdf