We did have one lunch at a place in NO I found when my wife's artist friend was elsewhere that was pretty good, but it wasn't any better than 50 places near me here.
We really spent little time in Austin, I dimly recall having good food the previous time I was there for a game, but I was "in good hands". I liked Austin just fine, would go back. New Orleans, I would not return for anything less than some unrealistic payment. I really did not like NO at all.
We had a decent dinner in San Antonio somewhere near Riverwalk (which overall I thought was ... touristy, duh).
Cities where I have stumbled across really good food include Boston, SF, LA, Seattle, Louisville, Cincy of course, NYC, DC ... I give bonus points for food that is unusual, to me, interesting, as well as really good. We like a couple places on Hilton Head a lot, Savannah has some spots but is getting touristy.
A few times in the middle of nowhere we've stopped and had great good. Recently in Clarksville, GA we had a very good Cuban lunch. Mine was excellent, unusual to me, really interesting flavors, for not much $$$. Clarksville, GA, near my birthplace.