We live a little bit past Downtown New Orleans, but we don't mind driving Uptown for a snoball from Hansen's. My favorite snoball is the Ginger Cayenne (pictured) under their Special Flavors menu. You can even spot the spicy cayenne pepper sprinkled throughout, this flavor is definitely an unexpected experience, I love it. Hansen's makes their own flavors daily and they have the absolute softest ice. Ernest and Mary Hansen opened it in 1939 and it's now run by their granddaughter Ashley.
And you can treat yourself to a New Orleans Hansen's snoball from Spring to Fall.