Roppongi Hills itself is a case in point. The chic-and-sleek business, shopping and arts development close to the centre of Tokyo was completed in 2003. Billing itself as an "Artelligent City, where art and intelligence fuse", it offers a dynamic modern art gallery in the Mori Tower and, way below, a liberal sprinkling of street art (the likes of a gigantic bronze spider and several huge white coffee beans that act as benches). On a Friday night it is buzzing. Courting couples crush onto the observation floor as if crowds and views were vital requisites for romance. Down at street level office executives beetle into plush bars, pausing to window shop at Versace, Kate Spade, Max Mara and more.
For a less costly night out, make for the bewildering tangle of the metro and join the younger hordes heading for Shinjuku station and the myriad eating opportunities in this bright-lights-big-city area. Above a jangling amusement arcade is the bizarre and obviously very popular Buddha theme- restaurant. To welcoming whoops from waiters whipping up an atmosphere, you join (more) canoodling couples in a large, dark dining area surrounded by Buddha murals and dominated by a vast golden Buddha statue. It looks as if it is grimacing at the music being pounded out in an indeterminate language - Japanese, Chinese, English? It's impossible to tell. Seven Asian-fusion courses later (sweet and sour chicken with prawns; pork in pastry with a chilli dip; fried rice with spicy octopus), you retreat to your hotel to digest a weird and very wonderful taste of Tokyo.
Yet in daylight the city takes on an additional and altogether different mien. Planted at the feet of skyscrapers, Christmas-tree rooflines of tiered pagodas become apparent; on the metro you pass kimono-clad ladies taking brisk but tiny steps in slippers and white, split-toe stockings; in the Asakusa district crowds flock to the Senso-ji temple while Buddhist monks beg discreetly on street corners. Turn down a side street in this area and you may well find yourself walking past wooden houses whose porches are awash with pot plants. You don't even need to scratch the surface of modern Tokyo to discover a traditional, time-honoured take on life.
Across Tokyo Bay, Odaiba is one of the latest districts of the city to be developed: a Japanese answer to London's Docklands, although the reclaimed land has largely become a playground for city workers. On the state-of- the-art monorail from Shimbashi station, the journey here is impressive - an efficient swoosh above the water and through a very 21st-century cityscape. But for all the futuristic outlook, you quickly realise that this is retro-land. The Tokyo Decks shopping and leisure development, complete with man-made beach and replica Statue of Liberty, offers only Fifties- and Sixties-style restaurants and cafes. Nearby is the Oedo-Onsen Monogatari spa, a re-creation of traditional mineral hotspring baths - albeit with a special spa centre for dogs next door.
But it's the food that perhaps most reflects Tokyo's enduring delight in old-time Japan. There's a degree of respect bordering on awe for the proprietor of Hatsuogawa restaurant in the Asakusa district. This is a word-of-mouth place, its reputation out of scale with its size - booking is essential since there is room for only 12 diners at any one time. For three generations one family has been serving grateful customers eel grilled over hot coals and brushed with a sauce for which the recipe remains a closely guarded secret. And, as with other specialist restaurants, the choice of menu is limited: eel in varying portion sizes with or without eel liver soup and sundry pickles. Despite the popularity of the place, the current owner stubbornly refuses to expand or change anything that might alter the rustic atmosphere of his one-room wooden house.
For a wider flavour of traditional Japan, visit an izakaya, which loosely translates as pub, although it would be difficult to imagine British pub grub emulating the Japanese offerings in these establishments. Here you down beer and sake while eating anything from asparagus to scallops and sashimi. Over in central Tokyo near fashionable Ginza, one such crowded sake house is run by an Englishman resident in Japan for the last 18 years. At Shin Hinomoto, Andy Lunt has earned the approval of a great many locals because of his intrinsically Japanese cuisine and his emphasis on mouth- wateringly fresh fish. What's more, in a city where language barriers make many menus incomprehensible to visitors, it is refreshing to be able to talk through a selection of dishes such as cod, grilled sword fish and monkfish liver - a sort of winter fish foie gras.
In other restaurants you quickly find that guesswork over menus is fun, if initially daunting, and that if all else fails you can always indicate your preference by pointing at the relevant plastic food display in the window. When these curiously unpalatable-looking objects inevitably begin to exert a fascination, head back to Asakusa. Here, near the much-visited Senso-ji temple, Kappabashi-dori is a neighbourhood devoted to the catering industry, selling neon signs, crockery, chopsticks, toothpicks - and wide variety of plastic food models. Shelves groan with everlasting life-size sea bream, tuna sushi, shrimp tempura and, in an intriguing blend of innovation and tradition, plastic versions of spaghetti Bolognaise, hot dogs and plates of fried eggs.
You can trace why the city has become such a remarkable mix of the old and the new at the absorbing Edo-Tokyo Museum, housed in a complex that looks as if it has landed straight out of Star Wars. Here you learn how Edo, an early incarnation of Tokyo, became the power base of the country from about 1600; how, for more than two centuries it and the rest of Japan were effectively cut off from the rest of the world by order of the Tokugawa shoguns; and how during this myopic period the great cultural traditions of Edo art and literature developed. Even more strikingly, you start to appreciate what a phoenix-like city this is, frequently rising from the rubble of devastation. Subject to earthquake, fire and (during the Second World War) bombing, Tokyo has an extraordinary history of suffering almost total destruction, and then being rapidly rebuilt. It's as if the city itself has become a master of reinvention without losing its soul.
Buttu Trick-Bar, Daini Toua Kaikan 3F, 1-21-1 Kabukicho, Shinjuku- ku (00 81 3 5292 2206; www.ug-gu.co.jp). The UG chain's Buddha theme-restaurant offers a seven-course set menu for Y3,000 (pounds 15).
Hatsuogawa on Kaminarimon Nakadori near the Senso-ji temple (00 81 3 3844 2723) meals served noon-2pm and 5pm-8pm. Around Y1,600 (pounds 8) for a bento box of unagi (eel) on a small bed of rice with eel liver soup.
Shin Hinomoto, 2-3-3 chome Yurakucho, Chiyoda-ku (00 81 3 3214 8021). From Y650 (pounds 3.30) per dish
New Takanawa Prince Hotel 3-13-1 Takanawa, Minato-ku (00 81 3 3442 1111; www.princehotels. co.jp/ english) This 16-storey hotel is
and offers good views.
It is set in a large Japanese garden complex conveniently close to Shinagawa station.
From around Y16,200 (pounds 84) for a double room.
Grand Hyatt Tokyo, 6-10-3 Roppongi, Minato-Ku (00 81 3 4333 1234; tokyo.grand.hyatt.com) One of Tokyo's newest and plushest hotels, with 389 rooms and suites on 21 floors. Doubles from Y57,500 (pounds 300).
Le Meridien Grand Pacific, Odaibo 2-6-1 Daiba, Minato-Ku, Tokyo, 135- 8701 (00 81 3 5500 6711; grandpacific. lemeridien.com) Offering wonderful views over Tokyo Bay, this is reputedly the largest hotel in the capital, with 884 rooms. Doubles from Y17,500 (pounds 90).
For more information contact the Japan National Tourist Organization (JNTO), Heathcoat House, 20 Savile Row, London W1S 3PR (020-7734 9638; www.seejapan.co.uk; or email email@example.com), open 9.30am- 5.30pm Monday to Friday. Free maps and brochures are available here.