H-cues is a fun place, but the tables are a bit old, they're 8', and the lighting seems a bit substandard. Plus they only have four tables total so it's easy to have to wait at times. But they are non-smoking and they do host regular tournaments.
JOBs is very smoky, so I haven't been back in years. It's also in Madison which would make it an easy 45 mins from La Vergne. Fat Willie's in Murfreesboro is also very smoky. The one time I went there it was early in the day and no one else was in there, but the entire place still smelled like one giant ash tray.
TNTs might be closest to you, but they had without a doubt the dirtiest tables I've ever seen. The cloth looked some sort of blue/black hybrid there's so much gunk on there, and it all comes off onto your hand and then onto your stuff/clothes. I've been there once and will never go back.
MJs in Murfreesboro is non-smoking, clean, and very nice with a bar, music, darts and cornhole, and large TVs. But all 7' tables.