I can walk all day in a well made pair of dress shoes, so it's not a question of comfort. I've worn everything from C&J boots to AE to Lucchese ropers throughout New Orleans. Here's my advice:
1. Prepare for water. New Orleans can get wet, and even on the sunniest of days, there's standing water on numerous sidewalks and alleys.
2. Prepare for scuffing. New Orleans has an older infrastructure, and so its roads, sidewalks, and curbs reflect a less ADA friendly time. Walk long enough there, with enough Pimms in you, and you're going to kick a curb or stumble on a cracked path. It can be crowded too, so wear something you that you won't mind if someone steps on.
3. No new soles. Lots of uneven concrete, and you don't want to slip and break your wrist.
If it were me, I'd go with a nice leather boot like a chelsea or monk boot, with a leather or rubber sole. They're versatile enough for casual wear or dress slacks, hardy yet comfortable, provide alot of protection from the elements, and take a shining well when you get home. The only downside is that boots are heavy to pack. You can wear them on the plane I suppose.
This isn't unique to New Orleans, but my general policy is that travel is hell on clothing and shoes. The packing, stuffing, TSA, unpacking, hanging, repeated wears, increased outdoor exposure, increased walking, and increased physical activity mean that I don't bring ANYTHING on trips that I don't mind destroying, losing at the airport, or being relieved of by a mugger. That means the nicest watches, shoes, clothes, etc. stay home. You don't have to look like a slob, but your favorites should probably take a break and yield to your second tier selection.