I can also attest that the BNA AC is one of the best in the system, if not the best. In addition to hospitality and service, the club also originated an ongoing charity auction of guitars signed by celebs who pass through the club -- of which there are many, from all genres of music.
We all missed it when it was shuttered during the Great Pullback of 2003-06, when we had to make do with the Admiral's Broom Closet, a former crew office where they put the club's couches and big-screen TV.
RE food: Nashville is actually a food destination now -- I no longer have to tell visting friends to bring a snack. The airport choices have gotten better, but they're pretty generic, except for Tootsie's and Whitt's. But if you need vegetarian, there's plenty of red beans, rice and collard greens.