Nestled into the ribs of the newest Atelier Ace hotel, Maison de la Luz, is Bar Marilou, one of New Orleans’s first aperitif bars. It is a place flush with luxury. Red velvet curtains billow against red walls and brimming red bookshelves. Here, with its low, golden light glistening off marcona almonds and anchovies, is the last place one would expect to be able to afford a cocktail.

“New Orleans is the mecca of the cocktail…so we have a lot of resp...