I can answer that since I live in Nashville. There is no true luxury in Nashville or Memphis, yet. In Nashville The Hermitage is a classic old Southern hotel (but with modern rooms), and in Memphis The Peabody would be its equivalent.

Note that in Nashville, a new boutique hotel is opening soon.

[Full disclosure: it's owned by a friend of mine, and he definitely aiming at luxury as this forum would understand it in the context of a smaller city like Nashville that would not support a FS, RC or similar.]