Country Music Hall of Fame is great...I'm not a huge country fan but the impact some of the artists they feature in everyday music is quite fascinating.
Grand Ol' Opry...if you can catch a show its great.
Ryman Auditorium...where the original Opry was done. Great to see a show in or even just a tour.
And if the preds are still around in June...I'd definitely recommend you catch a game. I know that they seem to be on everbody's list about why hockey shouldn't be in the south...but the few games I was at were one of the funnest, high energy regular season games I've ever been to.