Evis tugs against her lead and faces a wall. The dog – a black and white English setter – doesn't seem to like the idea of getting on a kayak and exploring the waterways of Tokyo. I, on the other hand, think it's a great way to see a city known more for bright lights, neon signs and skyscrapers than for paddle-able canals and rivers. "People just don't think they can go on the river here," Yukiko Koezuka, owner of Tokyo Great Kayaking Tour, tells me as we push off from the bank in the business district of Kayabacho.
It's a warm day in Tokyo and it feels good to be out on the water. Evis sits for a while in the lap of her Japanese owner, Tak, but mostly moves about excitedly, curious to see what's ahead. Standing at the front of the kayak, she looks like a figurehead on a ship. "For our tour, it's our first dog client," Yukiko laughs.
The company, which also runs cycling tours, launched kayaking trips earlier this year. "From the canals and rivers, Tokyo looks very different," says Yukiko, as we paddle our two-person kayak along high-banked canals, under flyovers, past fishing boats and apartment blocks. "You've heard of the Skytree?" Yukiko asks as the canal opens out on to the larger, less calm Sumida river. "There it is." She points to the thin tower, Tokyo's tallest building, which opened last year.
The Sumida is busy with water buses, tourist cruises and fishing boats, their wakes rocking our kayaks as we make our way across. Back in calmer canals, I see a jellyfish drift by, then another and another, one every few metres. "Do you eat jellyfish?" I ask Yukiko.
"Yes, we like jellyfish, but not from this river: too dirty," she laughs.
Kayaking is rare in Tokyo; we're clearly a novelty. Women with parasols stop to watch us from bridges. Cyclists pause to take a peep. Old men lean over railings, nodding "konichiwa" as we go under bridges. Children giggle and wave from the banks, or shout "oi" from apartment blocks where lines of laundry hang.
The nine-kilometre route passes through Koto, a middle-class residential area. "The water's cleaner on this side of the city," kayaking guide Kosuke Moriwaki tells me. "The river can smell pretty bad sometimes. At the end, you realise your clothes smell pretty bad."
"Being in kayaks is like a behind-the-scenes tour," says Kosuke. "You see Tokyo in terms of how the city works, the water infrastructure. You see the historical Tokyo. Tokyo used to be a canal city."
In the office, we'd looked at a map of how the city looked in 1843. There were waterways everywhere. Many have since been filled in or covered by bridges and motorways, but during the Edo period, they were vital. "In the Edo period, this river we're on – the Onagi – was built to connect the sea to the town and Edo castle," says Yukiko.
"Kyoto was the capital back then and Tokyo was called Edo, which means 'door to the bay'. Water was very important. In the 1600s, Shogun [samurai leader] Tokugawa opened Edo as the capital of Japan. He ordered people to build the canals. It was necessary infrastructure for transporting people, for food, materials, everything …."
We paddle down the man-made Onagi. Herons perch on the banks. The black head of a cormorant bobs in the river. Men and teenage boys stand on corners, fishing. Yukiko nods in the direction of trees lining the banks. "Those trees in April and the end of March … the cherry blossoms are gorgeous."
On the return leg, we paddle an exciting stretch of the wide Sumida river. There's a statue on the bank, Japan's national poet Basho Matsuo, a writer of haikus from the Edo period. A futuristic capsule-like cruise ship, known as the "space ship", designed by the Japanese manga artist Leiji Matsumoto, motors upriver as we turn and make our way back to the start point. As predicted by Kosuke, we smell pretty bad.
In the afternoon, I walk around the popular Yoyogi Park. Couples in traditional Japanese dress are getting married among the crowds of tourists at Meiji Shrine. Outside the park, costumed teenagers – a mix of goth, glam and doll-look – pose for photos.
Next morning, I explore Tokyo on foot with local guide called Yuki Nomura. We visit the neon-filled "Electric City". "This place sold radio components after the Second World War," Yuki tells me. "But now it's a sanctuary for otaku [geeks] and subcultures." Toy shops here sell collectable animals in capsules, figurines from Western and Japanese comics, and the latest craze, a cardboard box-man called Danboard.
Young women dressed as maids stand in the streets, handing out leaflets for maid cafés where men are "treated like princes. The maids sing and play games. Men go to maid cafés when they want to be cured of stress." Yuki suggests a look at Tokyo's red light district, pointing out the male equivalent of maid cafés: "host bars", where young men with pop-star haircuts and tuxedos entertain women. A truck rumbles past carrying two tall pink- and green-haired fembots (female robots) on a trailer, advertising the nearby Robot Restaurant.
There is no shortage of curious sights in Tokyo. And now, having been a kayaker on the city's waterways (with a canine lookout), I've been one of them.
Graeme Green flew to Tokyo Haneda from Heathrow with British Airways (0844 493 0787; ba.com); other airlines fly to Narita. Inside Japan (0117 370 9751; insidejapantours.com) offers a four-night Tokyo package, including accommodation, transport, one-day with a private guide and airport transfer, from £529pp, excluding flights.
Kayaking with Tokyo Great Kayaking Tour (00 81 3 4590 2995; tokyokayaking.jp) costs 7,000 Yen (£46).
Park Hotel (00 81 3 6252 1111; en.parkhoteltokyo.com) has doubles from 28,875 Yen (£190), room only