Carnation Cafe (on Main Street) and Storytellers in the GCH are great TS breakfast locations.
My favorite QS are Hungry Bear Restaurant in critter country (the onion rings and sweet potato fries are excellent), the Boudin Bakery (great salads), and French Market for the ambience (but food is iffy). People really like the chicken fusili pasta at Pizza Port, but I don't really eat pasta. Bengle BBQ is good, but expensive. For special snacks you can't beat Ghiradielli for sundaes or beignets in NOS.
For TS you HAVE to eat at Napa Rose. If it's too expensive at least go to the lounge and indulge in a drink and appetizer. It's the greatest place ever! Carthay Circle is OK, good cocktails though. I have had good experiences at Storytellers for dinner and Tortilla Jos in DTD.
I personally have never cared for the food at Big Thunder BBQ, but the atmosphere is wonderful!