Weather is good in April/May - best time to visit, April is better than May, as May can start the humidity. Avoid June-Aug, and Nov-Feb (for future advice!) - all are too hot or cold for this Brit's liking. April/May, Sept/Oct are the best period of the year for Nashville from my personal experience.
Would reccomend a drive (2 - 2.5 hours ) to Mammoth cave national park if in Nashville- a great day out - but not good for thouse scared of confined places or heights. I'm scared of both, but once on a tour there is no going back!
Oh and try to get a Opry ticket for Sat night if there. Even as a non-country fan, I really liked that. The bars downtown are a bit touristy...
Best reccomendation though - is go eat at the Barbecue place called Edleys on 12th. It's a bit like fast food for the food, but has a good bar... best Barbecue I've tasted in Nashville.... Martins and Peg Leg Porkers are the 2nd/3rd best.... expect to need to queue at all 3 places.