Where Do The Pontelliers Live?

If I'm not mistaken, I think the Pontelliers live in a very wealthy part of New Orleans. We know this because of the lifestyle they live. If you're looking for a particular area within the city, though, I'm not sure that the answer is explicit in the text.

Kate and her husband lived in the insular Creole community of New Orleans;

"The Pontelliers possessed a very charming home on Esplanade Street in New Orleans. It was a large, double cottage, with a broad front veranda, whose round, fluted columns supported the sloping roof. The house was painted a dazzling white; the outside shutters, or jalousies, were green. In the yard, which was kept scrupulously neat, were flowers and plants of every description which flourishes in South Louisiana. Within doors the appointments were perfect after the conventional type. The softest carpets and rugs covered the floors; rich and tasteful draperies hung at doors and windows. There were paintings, selected with judgment and discrimination, upon the walls. The cut glass, the silver, the heavy damask which daily appeared upon the table were the envy of many women whose husbands were less generous than Mr. Pontellier."

We know that Madame Lebrun lived on Chartres Street.