I second this idea! We visited the CM Hall of Fame last summer - not CM fans - but the museum was great. Also went to "Studio B", which is where Elvis Presley recorded most of his music.
We only stayed in Nashville for a day, and those two things filled it up.
Gatlinberg was a tourist trap, no doubt about that, but was fun just the same. Again, we only spent a day. Mellow Mushroom (I think that's the name of the place.) had good pizza.