Thanks for the tips, everyone. We just came back from our road trip through the South.
Natchez, a sleepy, somewhat touristy town:
Biscuits and Blues - a good bar, good music, so-so food
The Pig Out Inn - excellent barbeque (real wood!), homey atmosphere, clean, good slaw too.
The Castle at Dunleith - very elegant but not artificially so; very good food but very expensive; warm but inexperienced service; all around a good place for a special occasion, I'm glad we went
The Victorian - (the B & B) excellent breakfast with imaginative baked goods (inc. quiche, bread pudding, etc.); comfortable, fun place to stay, too