Shaya and Saba are two of my favorite restaurants! City Park is great to explore and the open air sculpture garden there is really nice. And you can go to Parkway from there!
We just got back from NO with a 16 and 18yo. Loved this bike tour through Marigny and Bywater. Also recommed Backstreet Cultural Museum. And yes to swamp tours! https://confederacyofcruisers.com
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https://www.nationalww2museum.org/