What should we see outside the French Quarter?

So my wife and I went to NOLA last summer and loved it - the food and music especially. We stayed in the French Quarter and didn't rent a car and enjoyed the things you could reach on foot. But what else is in NOLA outside the French Quarter that we should see? We don't want to stray too far from the city, but would love to see things outside of the usual tourist fare. We will be there again in either October or November. Would love to get some recommendations from locals! Thank you in advance!!