Our specialty here is barbecue and meat-n-three, but the latter is usually only offered for lunch. Depending on where you're staying in/near Hendersonville, you might be near Center Point Barbecue on West Main, which used to one of the area's best barbecue joints. I had it again about 7 years ago, and it wasn't the masterpiece it had been, but still darn good. September's Cafe on New Shackle Island is supposed to be great, though I haven't eaten there.
If you're up for the drive into Nashville, there are dozens of superb restaurants, which you can read about in some of the threads from late April and early May. For a Southern experience, I suggest Martha's at the Plantation, which is in the carriage house of Belle Meade Plantation. Food's good, and you could tour the house and grounds. Get a reservation. It's way out West End Avenue, the main thorough through the western part of the city.