Kerem HaTeimanim and Lev HaIr

At Sabich Tchernichovsky, I'm holding heaven in my hands. Bulging with colour, sabich knocks all hazy memories of kebab out of the park: tahini-slathered pitta loaded with roasted aubergine and egg, piled with salad and amba, a piquant mango pickle. "It's good, huh?" Anat mumbles between mouthfuls. I'm too enraptured to manage more than a nod in agreement. After washing it down with lemonade, we head into Carmel Market round the corner. I lose sight of her more than once, my attention grabbed by the likes of garish flip-flops and huge trays of baklava. I hear the sound of oranges being squeezed behind me somewhere, from another direction the strains of Europop, all underpinned by raucous shouts in Hebrew and Arabic.

But one right turn and, almost unnaturally, the chaos gives into the quiet of Kerem HaTeimanim, or the Yemenite Quarter. Developed by the Yemenite Jewish families who settled in the area in the early 1900s, this calm, mostly residential part of town feels oddly disconnected to the bustling city that envelops it. Pastel-coloured houses are festooned with bougainvillea, cyclists stop for hummus at family-run cafes, and doorsteps are guarded by slinky, half-asleep cats. We call in for coffee at Yom Tov Cafe and then sweet, rose-scented malabi pudding at HaMalabiya.

Meanwhile, across the street, Lev HaIr — 'city centre' in English — is a bold hub of urban architecture. There are the clean lines of the Tel Aviv Museum of Art housing a collection of works by Israeli artists, but there's also the magpie of the architecture world. Fanciful and flamboyant, eclecticism borrows bits and pieces from other styles, with some of Tel Aviv's highlights being the Pagoda Building with its oriental flair, the exotic-looking Levine House, and the mustard-coloured facade of the bustling Hotel Montefiore.

But Tel Aviv serves up an even bigger architectural heavyweight. Off the main drag of Allenby Street, there's peace in Bialik Square, the heart of the world's highest concentration of Bauhaus buildings. When the Nazis shut down the Bauhaus School of Design in 1933, deeming it a bastion of illicit idealism, many of the Jewish architects there fled Germany and settled here, in what would become Israel. Bauhaus then rapidly and dramatically shaped early Tel Aviv's skyline, its design more practical than beautiful: straight lines to maximise space, flat roofs that could be repurposed, minimal decoration and a muted colour scheme to reflect the heat — it's this that earned this part of town the 'White City' moniker. On paper, it could all could err on the dull side, but a stroll through Lev HaIr reveals a subdued, harmonious beauty to this rather utilitarian art.

Florentin

'Stay hungry, stay foolish,' screams Prime Minister Benjamin Netanyahu from a piece of street art. Nearby, a miniature Alice in Wonderland is poised with a can reading 'Spray Me'. It's a brazen introduction to Florentin, Tel Aviv's most alternative district.

"There were lots of warehouses, factories, shops here that were derelict," says Ross Belfer. New Jerseyan-turned-Tel Avivian, he heads up Eager Tourist, which runs hyperlocal tours throughout the city. "So for the people who moved to Florentin, they had an ugly blank canvas to create their own community."

What was Tel Aviv's industrial quarter has now emerged as the city's hipster magnet, its once-cheap rents drawing arty upstarts who don't mind slumming it a little. Not that Florentin's much of a slum these days. Now a sought-after corner of town, it ticks along with an easy, effortless neighbourhood feel: at Yom Tov Deli, I peruse coloured tins of fish, dolma (stuffed vine leaves) and mounds of olives. Round the corner are swish tattoo parlours and furniture showrooms, little tailors crammed with clothes, vibrant bars on street corners and shops selling huge pales of loose tea.

"I know where we can go for something refreshing," says Ross. "Do you like vinegar?"

At Cafe Levinsky 41, the long-haired Benny Briga is chatting to customers in his truck-cum-seating area. Beaming, he offers us a gazoz. I confess I've never had one before, nervously eying the obscure jars and bottles stacked in his pint-sized cafe. Barista Lisa gets to work on the drinks. "The vibe here in Florentin is great," she says, yanking stems from a vase and stuffing them into a glass. "I came from Toronto to visit a friend and never left." And so she hands me a glass of gazoz — a tangy, vinegary, fermented kombucha-like beverage, dashed with fruit syrup and served with a healthy helping of flowers.

Lisa's not the only expat drawn in by Florentin's rough-diamond charm: the young tattoo artist I speak to down the street is Ukrainian, a waitress who serves me is Turkish, and I hear French and Russian in the streets. After all, multicultural Florentin even owes its name to a Greek Jew who first bought the land here.

From Casbah Florentin, the shabby-chicest of cafes full of twentysomethings with laptops, I watch as a woman unhurriedly cleans up after her pug on the pavement opposite. Florentin's no beauty queen, but she doesn't hide it. It's this unpretentious, in-your-face realness that keeps those laptop-tapping hipsters plugged in.