Although Narita Airport is the name most associated in travellers' minds with Tokyo, the formerly domestic-only Haneda Airport has been available to international passengers since 2010.
Would you rather travel 57km by bus, train or taxi between airport and city or 14km?
But it's not quite that simple for Australians. Only some international carriers land at Haneda, including Singapore Airlines and Thai Airways.
My Thai partner, Ittidet, and I are able to arrive at Haneda by flying All Nippon Airways (ANA) from Bangkok. We stay at the ANA InterContinental Hotel, just minutes from the Ginza subway line and with a distant view of Mt Fuji from the 36th floor.
Had we landed at Narita, we would have missed the auspicious full moon lighting up a pre-dawn sky and reflecting off Tokyo Bay on a clear winter morning in January.
Where to begin exploring this gigantic city of 13 million people that spreads from Tokyo Bay in a conurbation spliced by three rivers?
We choose Senso-ji temple, which was built about 645. Legend has it that two fishermen, who were brothers, caught a statue of a goddess of mercy in their net and a decision was made to build a temple there.
A big red lantern marks the "thunder gate" entrance to the temple and also ground zero from which the city was to expand.
Late-afternoon midweek, it is crowded with domestic tourists. I succumb to an artistically wrapped red-bean sweet - and so begins a food journey that is as rewarding as the trip itself.
Every restaurant meal, snack and pastry is completely satisfying or contains some intriguing taste or texture to make it worth trying. From slim soba noodles to slippery flat udon, shaved beef to grilled saba tuna, teriyaki chicken to sizzling yakiniku (barbecued) pork - it is all distinctively Japanese.
I have to try sake and it is warming on a chilly afternoon. But draught beer is the perfect accompaniment to the usually salty food.
It is a personal triumph to get Ittidet - with his attraction to fashion, cut, brand and fabric - into not just one but two museums.
We even reach the gates of the Metropolitan Teien Art Museum at dusk on our last evening after a shopping marathon only to find it closed for renovation.
I immerse myself in Japanese art with the glories of the Tokyo Museum - a collection which includes very ancient pottery, spare Zen paintings, fabulous lacquer work, embroidered costumes and wooden masks. It's not to be missed.
Another must-see is the sublime collection of Western art close by at National Museum of Western Art. Be prepared for the great Rodin sculptures that grace the forecourt and an entrance hall - the Burghers of Calais, The Thinker and the large erotic Entrance to the Gates of Hell ("Come in," it calls. "Come in . . . ").
The museum's collection also includes Monet waterlilies and yellow irises, Dutch landscapes, a veiled woman by Renoir and works by Picasso, Miro, Brueghel, van Gogh, and Gauguin, as well as Renaissance Italian paintings.
A Western art collection makes perfect sense after I read about Emperor Meiji's efforts to open his country to Western influence in the second half of the 19th century (the Meiji Restoration).
He acceded at the age of 17 and, as a symbolic gesture, cut off his top knot, began wearing Western clothes and drinking wine with meals.
He was not only an innovator but also a true man of the people and was responsible for moving the capital from Kyoto. So it is fitting that he and Empress Shoken are still revered at Meiji Jingu Shrine.
When we visit Meiji Jingu on a Saturday, it is simply a matter of following the crowds from the entrance at Omotesando station.
People line up to make wishes and pray in the large main courtyard and we see two weddings there.
The key to exploring Tokyo is to get to grips with its subway and train system with 36 different lines.
Sudoku-loving Ittidet sees it all as a puzzle to be solved and away he goes, with me tagging along, trusting his unerring spatial intelligence. Apart from a couple of minor mistakes, we never get lost. All-day passes are good value at just over $7 and the trains are punctual and clean but crowded.
Ittidet has heard about Takeshita Street in Harajuku, near Omotesando and Harajuku stations, where young eccentrics gather and shop. It makes for a crowded, entertaining 400m walk before we end up on the stylish tree-lined boulevard of Omotesando which is packed with smartly dressed shoppers.
I had thought Ginza was an entertainment district but, in fact, it is high-end shopping with an architectural jewel at its heart - the neo-Renaissance granite Wako building and clock tower. The handsome curved seven-storey structure dominates one corner of a busy intersection.
If Ginza is money and style, then Shibuya is crowds and pulse. This is where four streets intersect and the sea of humanity parts and rejoins according to the walk/don't walk signs. It is great to be part of it but to really immerse yourself in Japanese culture you must wash with them - naked - in a bathhouse called an onsen.
What does it matter that the one we go to - Ooedo - has a somewhat theme-park atmosphere reproducing an Edo-era village?
Following our Tokyo Handy Guide, we take a monorail at sunset along the foreshore, then over the Rainbow Bridge, getting spectacular views of the city, Tokyo Tower and the bay along the way.
Our timing is perfect. The price drops 400 yen (nearly $6) at 6.30pm, so we have less than half an hour to wait before other local bargain hunters who know the system begin to arrive.
First you choose and change into a printed full-length cotton yukata. After genders are separated you take that off and leave it in a locker with your underwear, left with nothing more than a small yellow towel.
Finally, you join the other men (if you're male) in the ritual washing, scrubbing, mineral-water soaking and sauna. Most of this takes place indoors but the best part for me is sitting in a hot pool outdoors and looking at the stars starkers.
There is time for just one trip out of Tokyo, to Kamakura, about 50km south-west where there is a big bronze Buddha statue near the city.
We go on our first day and find time to visit Yokohama in the evening on the return journey.
There is a resonance with the March 2011 tsunami when we read that the buildings around the bronze Buddha, built in 1252, also had been destroyed by a 15th century tsunami and that the base was damaged in a 1923 earthquake.
The hollow statue is more than 13m tall and was once covered in gold leaf. It is considered a marvel of early engineering but has benefited from modern techniques to ensure it will withstand future earthquakes.
Ittidet, who has Chinese ancestry, is keen to visit Yokahama's Chinatown. The artistry of its subway station, where old photographs have been superimposed on the wall, impresses me most.
Yokohama was the first port opened for trade in 1859 after Commodore Matthew Perry had used gunboat diplomacy to lift the silk curtain so that a pre-civil war United States could trade with its Pacific neighbour. The Meiji Restoration would occur nine years later.
Western influence has been strongest here and we see one example of beautifully restored and earthquake-proof architecture - the century-old red brick warehouse.
From Chinatown, we follow a bayside walkway beside a park to the city centre. A huge illuminated rollercoaster and fun park finish the walkway.