I live in Murfreesboro. It's gotten really hot here, especially for multi-family. Not quite as much as Nashville but prices are skyrocketing.
Atlanta is 4 hours away so that is not really a consideration for the Nashville market. Chattanooga is 2 hours away. It's not really involved in the Nashville market either, other than some investors putting money there, but has a pretty good infrastructure and investment options. Just be careful of the areas you do invest there. Huntsville is a 1-1.5 hours away. It would be more of a tertiary market for Nashville. But a couple Nashville investors that I know of are moving money down there as well.
If you were looking more for stable rent with smaller multi-family, it might be good to look north of Nashville in the Clarksville area. Because the large army base is there, there's always going to be consistent demand. I don't know anything about the appreciation though like Nashville/ south Nashville areas has. Clarksville is between 45 minutes to 1 hour away from Nashville.