“Is much better! The tourists is coming back!” That was our cab driver from Louis Armstrong Airport into New Orleans — a transplanted Haitian from Jefferson Parish. But the signals were mixed during the first of the 39th annual New Orleans Jazz & Heritage Festival’s two weekends (April 25-27 and May 1-4). At the chic bistro Herbsaint, our waiter, a transplanted New Yorker who’s lived in the city for 10 years, said he and his fiancée have been telling each other ever since Katrina, “We have to get out of here.” He’s studying to be a trauma nurse, she’s a graduate student in education. A house that would have cost them $95,000 before the hurricane would run them $265,000 now. And the city’s long-time chronic problems would be the most dispiriting for anyone in their professions: for her, widespread illiteracy, and for him, “Most of the traumas we see are gunshot wounds.”

In a way, it’s the same old story for New Orleans — every day, it seems, another murder. On Saturday, the Times-Picayune reported three people shot in a home invasion about eight blocks from the Fair Grounds Race Course, where the festival is held. It was termed a “targeted attack” — masked gunmen dressed in black, leaving two dead at the scene, wounding another who died later at a local hospital. They were the 62nd, 63rd, and 64th murders in the city this year (compared with 20 in Boston as of April 21).

There are, of course, the signs of improvement. The Lower Ninth Ward, which took heavy damage from the breach in the Industrial Canal flood wall, is virtually wiped out — former neighborhoods now nothing but weed-grown lots, with only a few signs of rebuilding. The Upper Ninth is faring better, buoyed most of all by Habitat for Humanity’s Musicians’ Village, several dozen shotgun-style homes in bright Caribbean colors on neat plots, rockers on the front porch, rosebushes facing the lawn. A new street — and more houses — are under construction. And around the Village, there are more signs of renovation. But for every home that looked pretty as a French Quarter postcard, there were two that were collapsed or abandoned, the tic-tac-toe spray-painted codes of the Katrina rescue workers still visible.

In the Central Business District adjacent to the Quarter, one sees fewer boarded-up buildings and more construction. The Footlocker at Canal at Bourbon Street — which was boarded up the year after the storm, and where my wife and I watched the To Be Continued Brass Band play a great set — is up and running. (And though we didn’t see the TBCs this year, they had taped a cardboard sign to the store’s side.) The Quarter, of course, looks to be thriving — the one indicator that the city is still suffering from a lack of a resident workforce is that late-night spots like Coops and the Clover Grill aren’t back to their former all-night hours. Across Canal, in the Central Business District, the Donald has signs up in the lot down Poydras Street from the venerable Le Pavillon hotel for a new Trump International Hotel & Tower.

Of course, a New Orleans that’s all luxury condos wouldn’t be New Orleans any more. Jazzfest has always given its audiences the home-grown along with the big names — this year Billy Joel, Sheryl Crow, Alison Krauss & Robert Plant, Tim McGraw, Jimmy Buffett, Stevie Wonder. What New Orleans has — what fosters its special culture — is community and continuity: the Mardi Gras Indians, the brass bands, the Social Aid and Pleasure Clubs. These traditions have emerged from some of the city’s most desperate neighborhoods. As local WWOZ radio announcer and historian Tom Morgan told me two years before Katrina, “If you say you’re from the Seventh Ward, that means something. The Ninth Ward is where Fats Domino is from — and everyone knows that.”

The names of ancestors mean something too. Not just Fats but also Danny Barker, Anthony “Tuba Fats” Lacen, Big Chief Allison “Tootie” Montana. These weren’t just musicians, bandleaders, and Indian chiefs — they were teachers who passed on traditions. Playing on the WWOZ broadcast of its annual “Piano Night” from the House of Blues the Monday after the first weekend of Jazzfest, pianist David Torkanowsky dedicated a song “honoring one of the village elders who passed away last year, Alvin Batiste.”

Now, many of the living names and generations are scattered from Houston to Western Mass, and bands on stage often give an inventory of their members — who’s moved back, who will move back, and who’s still living in Dallas. On stage at the festival, the Indians in their elaborate feathered and beaded suits were represented by multiple generations, from the ancient to pre-teens. In the Fair Grounds grandstand on Saturday afternoon, Tootie Montana’s son Darryl — now himself Big Chief of his father’s Yellow Pocahontas — stood by an exhibit of suits and photographs and talked to a handful of tourists while the relentless Louisiana rain poured down outside: “I learned how to sew from my father when I was six. I made my first suit when I was 11. I’m 53 years old now.” His elaborate Mardi Gras costumes are sought by museums.