My four-year-old daughter, Ruby, is perched on Father Christmas's capacious knee, listing the things she would like: "… and then perhaps a Barbie, or maybe a horse, or a book …"

Father Christmas smiles, lifts her down and says, in a strong Cajun accent: "Well, if you've been a good girl, then sure the presents will come."

Outside the window a horse thunders past the winning post. Father Christmas turns to his elves: "Did anyone think to have money on that?"

Welcome to Christmas New Orleans-style. We're at the City's Fair Grounds Race Course, one of the oldest racetracks in America, for its family Christmas Day, an entertaining if chaotic mixture of arts projects, cake decorating and – for adults only, of course – gambling. While the kids race from table to table, making beaded necklaces and listening to a Cajun version of The Night Before Christmas, I watch local boy and triple Kentucky Derby winner Calvin Borel ease his horse home and wonder if I've been in a more incongruous situation all year.

New Orleans probably isn't the first place you think as a family Christmas destination. It's a city best known for its laid-back charm and partying ways, a place you go to have a good time without small voices telling you that they're tired and need food. American friends were horrified when they learned of our plan: "Why would you take your kids to New Orleans? People don't take their kids to New Orleans… They go there to have a great weekend away from them."

I didn't listen because I had a dream. Ever since we moved to New York, four years ago, I've been secretly disappointed by the city's attitude to Christmas. Yes, the light displays in midtown Manhattan are gloriously over-the-top and, yes, the Fifth Avenue shop windows rivalled those in London, but where we live in Brooklyn there is more brouhaha about Halloween, and the bone-deep pragmatism of the native New Yorker means it's not uncommon to see Christmas trees tossed into the gutter at 8am on Boxing Day as everyone returns to work.

This year I wanted something different. Something more celebratory, with bells and lights and carols: the full over-the-top Christmas deal. And in gaudy, glorious New Orleans, that most catholic (and Catholic) of American cities, I had an inkling I'd find it.

It's 7pm on 16 December and my family and I are surrounded by the largest, most intricate Christmas light display we have ever seen. There are Spanish oak trees decorated to look like falling snow, crocodiles made from thousands of green lights and an entire Who Dat? tree given over to local American football team the New Orleans Saints. This is Celebration in the Oaks (celebrationintheoaks.com) at New Orleans City Park, an annual extravaganza of music, songs and, most importantly as far as my two children are concerned, fairground rides. While my husband and I listen to Cajun and Zydeco versions of Christmas carols, the kids have annexed the monkey drop ride and are repeatedly shooting up into the air before plummeting back down yelling, "More, more! Again, again!"

Chaotic, exhilarating and ever so slightly kitsch, Celebration in the Oaks sums up everything that's most wonderful about New Orleans. Six years after Hurricane Katrina wrecked this city, the scars are still visible – as we walk from the Fair Grounds to City Park through the seventh and fifth wards it is impossible to ignore the still-abandoned houses, the uprooted trees, the graffiti commemorating the dead. Yet it's also impossible not to celebrate the city's resilience, and its unexpected moments of beauty.

Rounding a corner near Fair Grounds we glimpse a Mardi Gras Indian in full costume talking intently to a group of friends: it's like some lost scene from the Treme TV series. As we walk through the French Quarter on a quiet Sunday, a car squeals to a halt and the driver yells "Heads up kid" at Ruby before showering her with Christmassy coloured beads; and on Pirates Alley, near the Faulkner House bookshop, my son Oisin was entranced by an eight-piece jazz band in Santa hats and tinsel.

We spend Saturday strolling through the French Quarter. With all the talk of New Orleans as party town people rarely consider it as a child-friendly destination, yet it is one of the most welcoming US cities we've visited. Restaurant staff, whether in high-end joints or dimly lit po-boy shacks, fall over themselves to accommodate us; museums, from the lovely Louisiana Children's Museum (lcm.org) on Julia Street to the enjoyably creepy Insectarium (auduboninstitute.org) on Canal Street are easy to navigate and wonderful to waste time in; and, best of all, the streets are full of free music. Our two- and four-year-olds dance exuberantly to everything from mournful blues to wild jazz.

It helps, too, that we have an expert guide. Before we flew out my husband asked actor Wendell Pierce, of Treme and The Wire fame, on Twitter if he had any recommendations. Pierce, a passionate advocate for his hometown, answered instantly with a stream of recommendations, almost all of them geared at a family with young kids.

He was insistent that we get tickets for the Preservation Hall's Creole Christmas (preservationhall.com), and from the moment we enter the dark, cosy venue and squat on the floor in front of the band we know Pierce was right. For an hour-and-a-half we lose ourselves as old standards like Santa Claus is Coming to Town and Silent Night are rendered fresh and newly appealing by the venue's famous St Peter Street All-Stars. It's a rollicking yet intimate show: our two-year-old goes from attempting to escape to swaying gently, lulled by the trumpet's purity and power.

Then there's the food: oysters in absinthe at Commander's Palace (+1 504 899 8221, commanderspalace.com) in the historic Garden District; a surprisingly lovely gumbo in a French Quarter tourist trap. New Orleans is a food lovers' paradise. We eat simply fried fish near Treme, devour po-boy sandwiches dripping with meat and gravy in the Marigny neighbourhood, and are blown away by the adventurous menu at the tiny Green Goddess (+1 504 301 3347, greengoddessnola.com) on Exchange Place, in the French Quarter.

Best of all as far as the children are concerned are the beignets. These warm doughnuts dusted with sugar are the biggest hit of the holiday. We eat them sitting outside Café Beignet on Royal Street listening to a man in a wolf mask playing the violin. With the sounds of last night's carols faintly echoing in my ears, I gaze at the pretty, painted houses bowed down by tinsel and glittering fairy lights and feel my Christmas dream come true.