My husband and I haven’t missed a Jazz Fest since Katrina and we lived in New Orleans for three months in 2011, so we often get requests from friends about what to do. I’ve compiled an ever-expanding list to share when someone asks.
These are my NOLA tips — I welcome your additions, questions or objections:

In general, New Orleans is more a state of mind than a place. People move slower, they’re less concerned with what you do than where you ate last night, music and art are everywhere and there’s such appreciation for creativity … so don’t worry as much about your to-do list as about experiencing how it feels to be there.
Do an obligatory walk down Bourbon Street one night, maybe on your way to something more your speed. It’s a younger, drunker, rowdier crowd than I want to be part of, but it’s worth seeing a never-ending street party.
Much of the best music we’ve seen has been unplanned. If you stroll down Royal Street during the day, for example, a fantastic band typically plays on the street in front of Rouses grocery store. That’s sort of what New Orleans is about: serendipity.

That said, as a traditional jazz fan, I suggest Irvin Mayfield’s for a civilized happy hour, Fritzel’s on Bourbon Street for a little later in the evening, and Spotted Cat and/or dba on Frenchmen Street at the end of the night.
Wednesday night, go to Preservation Hall on St. Peter just off Bourbon. It might be hot. There’s no AC. There are very few seats and they don’t sell drinks, so wear comfy shoes and get the obligatory hurricane to go from Pat O’Briens next door. But Preservation Hall Jazz Band is typically in town Wednesdays and the hall is unlike anything else I’ve experienced. It’s like a temple to trad jazz.
John is a sazerac fan and he really loved them at Old Absinthe House and at Napoleon House, both in the Quarter. The Sazerac Bar is beautiful and just a short walk from the Quarter in the Central Business District.
Have a drink at Lafitte’s Blacksmith Shop on the far end of Bourbon Street and sit on the sidewalk if you can. (You’ll find that with no open container laws, you can just get a drink and stroll wherever you want with it.)
St. Claude is to New Orleans as Bushwick is to Brooklyn. It’s the younger, edgier entertainment district. The All-Ways or the Hi-Ho can launch an evening there, or maybe you’ll end your night at Spellcaster.
Coop’s has crazy-good Cajun-inspired pasta and is among the best fried chicken in town. There generally a line, but the bar next door, Molly’s, has friendly bartenders and delicious frozen Irish coffee, so you can get a drink in a go cup and treat the line as your happy hour.  Service can be a little gruff at Coop’s but they deal with drunks, tourists and drunk tourists all day so I don’t take it personally.
Related: Molly’s has good free wifi and several outlets, so if you must do a little work, it’s a pretty great remote office.

Of the well-known restaurants in walking distance of the Quarter, I would do lunch at K-Paul’s (they do a cheap self-service lunch that I liked better than dinner) and  dinner at Emeril’s (because I don’t care how cliche bam became, the guy still knows his chow). Galatoire’s is an institution, jackets required, excellent people watching and nola.com says the new chef is improving the food, though that’s almost secondary to the scene.
John’s favorite roast beef po boy is at a divey bar called Parasol’s in the Irish Channel, adjacent to the Garden District. You could take the St. Charles street car for an afternoon ride and hop off for a meal. Also, the firecracker shrimp po boy at Parasol’s is so delicious.
People will tell you to go to Cafe du Monde for cafe au lait. It’s iconic and open 24 hours so it can be worth doing. I think Cafe Beignet on Royal Street is better. Besides good coffee and beignets, which are heavily powdered doughnuts, it has a side door that opens to the police department … a short cut for cops to get doughnuts? C’mon. That’s beautiful.
Take the St. Charles street car to see the big old houses where the wealthy folks live, then if you haven’t seen the devastation and reconstruction in the Ninth Ward, get a cab or a tour through the Brad Pitt houses (formal name is Make it Right) and the Musicians Village Habitat for Humanity neighborhood.
If you get ambitious, taking a swamp tour might be touristy but it’s an interesting insight into a totally different way of life and ecosystem. You’ll lose much of the day, with the bus ride out and back, but if you have the time, it’s a nice reminder that there’s more to Louisiana than Bourbon Street.
Related posts on Newvine Growing:

• Katrina spurred me to visit – and fall in love with – New Orleans
• I didn’t expect to like New Orleans Jazz Fest, but it surprised me
• Tim Robbins on some of what makes New Orleans special
• Goin’ to New Orleans: sinking in to a city we love