The Bistro at Maison de Ville is on Toulouse. It is a hidden gem.
Irene's is on St. Phillip, just off of Chartres...most probably my favorite spot in the FQ.
Very casual: Verti Marte and Mona Lisa in the 1200 block of Royal.
1201 Royal St, New Orleans, LA
Mona Lisa Restaurant
1212 Royal St, New Orleans, LA 70116
539 Saint Philip St, New Orleans, LA 70116
OK, but think that I would have stuck with the OP, and just expanded the area slightly, but that is just me.
Galatoire's for NOLA, grand dame cuisine
G W Fins for NOLA influenced seafood (a tad more casual)
Arnaud's for nice NOLA cuisine, but a step below Galatoire/s
Antoine's, and if the recent reports are correct, then almost up to Galatoire's
Not sure what works for you, but those are my immediate recs.
209 Bourbon St., New Orleans, LA 70130