There is a mystique about the French Quarter. Traditionally, it is one of the few real bohemias in this generally utilitarian country. The Quarter has long been a favored haunt of artists, poets and writers—and just about everybody else who didn't fit in. As recently as the early '70s, it was a kind of colorful arts slum, and most of the major galleries were located there.

Now the Quarter is slicker and more touristy, and while some of the old scene still lingers, the major galleries are n...