If you don't mind an hr or so drive you may try Biloxi/Gulfport, MS or one of the neighboring cities. Amite, Hammond, Slidell, those are a bit over an hr also from N.O. There is a good safari in Loranger - not one of those drive throughs-you take their transportation out-love it in cooler weather.
But, if you want the full experience, stay downtown. Don't leave ANYTHING in view in your car-NOTHING- no matter what.
I live in NELA but used to live NOLA and visit my daughter often, so I know what I am talking about.