Nashville is one of those rare places where the best times to visit are not necessarily the best times to visit. Summer is appallingly hot and humid, with daytime temperatures approaching 100F, and the nights are sweaty and uncomfortable, so with common sense, the locals put all their best events and country music festivals on through the hottest months of the year, from May until September, and if you want to get all rootin'-an'-a-tootin', then this is the only time to go in order to see the biggest names in music, and sweat like a spit roasted pig with something awful on its conscience while you do it.
Weather wise, the most pleasant time to visit is in March or October, when the temperature falls to a much more pleasasnt 70F, and you can walk around without fainting. Sadly, there is not so much music on.