http://www.yelp.com/search?find_desc=bbq&find_loc=Nashville%2C+TN&ns=1
As far as "best", once you've had a good amount of bbq; it becomes a matter of taste and what bbq meat/prepearation you are looking for and in what style.
I would assume though in nashville, you're mainly going to get memphis style bbq.
TN has a huge bbq history, enough that it has it's own style; so even an "average" bbq I bet is going to be pretty good.