There is a lot of good riding in the Mount Juliet area. It all depends on how much traffic you are willing to endure but you can find plenty of traffic free roads to ride on.
I rode with the Mt.Juliet women's group last year. The ride left from a park over by I-40. Most of the rides were rather hilly but not much traffic. Also the main road from "downtown" out to I-40 has a new bike lane. Depending on which part of Mt. Juliet, you can always head toward Gladeville or Lebanon/Watertown. My sister lives in Mt. Juliet and I can get a great 60 mile round-trip from Smyrna via the Glade. Check the Veloteer website for some of their favorite routes. http://www.veloteers.org/