I can't suggest a particular shoe, but wear something comfortable. Parking is tough in the French Quarter and you end up doing a lot of walking. New Orleans tends to get kind of wet too so you might want to rethink suede.
Check out Bywater barbecue while your down there. Good food, no lines and not too expensive.
https://www.frommers.com/destinations/neworleans/D63759.html
CCs has great coffee, Rue de la Course on Magazine is an uptown cafe in where a lot of locals hang out.
DBA on Frenchman is a cool little bar with a huge beer selection and has great local bands. (Frenchman is just outside the quarter - facing cafe du monde take a left until you come to a fire station.) There are a lot of cool jazz clubs on Frenchman as well.
One eyed jacks on Toulouse has a kind of secret upstairs called the matador room where celebrities sometimes hang out.
If someone bets you they can tell you where you got your shoes, well.... I'll let you figure that one out for yourself.