In the ultra-hip backstreets of Tokyo’s high-end Aoyama district, it’s impossible not to feel deeply unfashionable. A string of chic boutiques sits between swanky jazz clubs and bank balance-bashing restaurants. Prada and Miu Miu bags hang from arms. Security guards stand sentinel outside the fanciest shops. But seeing as Aoyama’s most stylish stores also double as stunning examples of the best of modern Japanese architecture, thankfully there’s no need to linger inadequately over the designer goods.

Instead, a walk around the area presents a free and revealing way of exploring a city which can rapidly drain even the healthiest of travel budgets. Because here in Aoyama, the world’s top-end clothing brands appear locked in a battle of one-upmanship. The likes of Miu Miu, Gucci and Dior have teamed up with world-class designers to transform the area into a living architecture museum. But perhaps you could also say it highlights Japan’s tendency to create the exemplary out of the ordinary. Due to earthquake fears and a culture of disposability, buildings here are torn down and rebuilt every 30 years on average, the country constantly in thrall to the new.

The Herzog & De Meuron-designed Prada building in Aoyama represents the area’s stylish reputation (Sota/Flickr/CC BY-SA 2.0)

“There are so many beautiful buildings here,” says Professor Tsutomu Matsuda – or Mazda, as he prefers to be known. “The area changes every year. It’s hard to keep up.” Professor Mazda is spending his Saturday afternoon showing me around Aoyama’s most notable buildings as part of a private tour arranged by the Palace Hotel Tokyo. Mazda runs his own design agency and is the author of two architecture walking guides of the city, so there’s probably nobody better suited to the job. (For those who can’t stretch to the cost of a flight, London’s new Japan House, opening in 2017, is set to showcase the very best of Tokyo’s design in the UK, and make Japanese design our capital’s next hot trend alongside ramen and yuzu.)

The professor stops in front of the From First Building, its Lego-esque blocks nothing like the average, prefab high-rises the world associates with the Japanese capital. A masterpiece of deconstructed architecture, the split levels and staircases give you the feeling of being inside an Escher painting. Posh stationery shops and furniture stores vie for business. Mazda instructs me to peer up at its skywalks and open structure, the blue skies of this Tokyo afternoon brightening the building’s corners.

The Tokyo Tower is a highlight of the city’s busy skyline

“This is what started it all,” he says. “It’s like being inside when in fact you’re outside.” Mazda says the building’s kooky looks inspired the other wild and wacky creations that have sprung up around Aoyama’s Omotosando-dori in the past decade. These include Fumihiko Maki’s Spiral, a gallery and stationery store which gives more than a passing nod to New York’s Guggenheim, and the all-glass Dior building, created by the SANAA agency, where the ceiling heights vary and the glass walls throb with white light.

Thanks to the Olympics, architecture is a hot topic in Japan. The original, Zaha Hadid-designed stadium was controversially scrapped in July last year, with local architect Kengo Kuma’s more traditionally inspired wooden theme chosen instead. When commissioned to redesign the stadium, Kuma said he wanted to build something that represented Japan now – wood, rather than concrete, he claimed, represented the post-industrial society Japan has become.

Although Kuma’s stadium is yet to be constructed, his work is dotted around Aoyama. If it’s clad in fresh timber or bamboo, there’s every chance it’s one of his creations – he has spoken of the importance of wood in his work and Japanese culture, and how it invokes tranquillity. Most famous of all is his Nezu Museum. Built in 2010 and home to a collection of pre-modern Japanese art, it was designed as a modern take on the Japanese ryokan, or inn. “Japanese buildings are approached indirectly, rather than through a front door,” says the professor, leading us down a bamboo-lined walkway towards the museum’s entrance and traditional gardens.

Nezu Museum is Japanese architect’s Kengo Kuma’s most famous design so far (Yuya Tamai/Flickr/ CC BY 2.0)

There’s a sense of calm here you’d expect to find high up in the mountains of northern Japan rather than downtown Tokyo. It’s easy to see why Kuma was chosen to remodel Tokyo’s Olympic stadium in the country’s more traditional and spiritual image. When I mention this to Professor Mazda, he grins, runs a hand through his long white hair and turns. “Follow me,” he says. “I want to show you something totally different.”

We walk another five minutes through anonymous backstreets before it emerges, all wooden shards, a sharp contrast to everything around it: Sunny Hills. This has to be the world’s most out-there cake shop. Unlike the traditional Nezu Museum, it has an irreverent feel to it, its timber triangles, both inside and out, designed to look like the Taiwanese pineapple cakes they serve up inside. It’s joyous and extremely silly.

Sunny Hills might have the most original exterior as far as cake shops go (Sunny Hills)

Energised by the sweet treats and fresh matcha tea, the professor moves us on quickly, using his walking stick to point out details on an array of Aoyama’s most surreal and brilliant buildings. Herzog & De Meuron’s Prada store is a riot of angular beams and reinforced glass, which the professor explains defies Tokyo’s usual approach of using strong concrete beams to prevent collapse during an earthquake. The reinforced rhomboid structure is designed to move when the earth shakes, allowing it to withstand any after-shocks.

The Prada store incorporates strong concrete beams into its design to prevent collapse in the event of an earthquake (Chinnian/Flickr/CC BY-SA 2.0)

I have just a few moments to baffle Prada’s staff by strolling past pricey handbags to snap shots of the spectacular interior before my guide beckons me to follow him towards the singular Omotosando Hills shopping mall, our final stop. This is nothing like the cookie-cutter shopping centres you find off of motorway junctions. Its sharp corners and the ruler-straight lines of the overhead walkways were designed by the self-trained Taduo Ando.

The Omotosando Hills shopping centre features a cascading waterfall of staircases

Watching as shoppers stroll down a waterfall-like central staircase, it’s easy to see why the professor is so in love with his hometown’s architecture. Idiosyncratic, brilliant and bizarre, it represents everything that’s great about this soon-to-be Olympic city.

Travel essentials

Getting there

British Airways (ba.com) flies twice daily from Heathrow to Tokyo. Prices start from £692 return.

Staying there

Palace Hotel Tokyo (en.palacehoteltokyo.com) offers a three-night bespoke Transcendent Tokyo itinerary from £2,090 per person. Includes B&B and a full-day, expert-led art and architecture tour of Tokyo. The hotel's concierge team can individually tailor tours according to a guest's interests.