There are many sides to Japan. Much of Tokyo had to be rebuilt after the World War II bombings; hence the city's futuristic feel. But Kyoto retains the stately aura of Japan 's imperial heritage. Or to put it another way; Tokyo inspired Blade Runner and Kyoto inspired Memoirs of a Geisha.
And the country's volcanic south is a world apart from both the gentility of Kyoto and the techno-trendiness of the capital. Kyushu Island, home of the blowfish and many mineral rich hot springs, is a couple of hours' flight from Tokyo. Or if you don't mind moving almost as fast on land, you can take the(blurry) scenic route on the famous bullet train.
Wherever you decide to go, there are plenty of things to see. Sumo wrestling and kabuki theatre are two of the better known spectacles, enjoyed by tourists and natives alike(particularly sumo - its champions are major stars and, indeed, sex symbols). Golf is also big in Japan.
The country's major belief systems, Zen Buddhism and the state religion of Shinto, have deeply influenced its art and culture. Matsuri, or festivals, are a major draw throughout the year. There'll be one happening whenever you choose to visit, and many of them sound like they were thought up after one sake too many: try Tokyo's New Year festival of Dezome-Shiki, where firemen do acrobatics at the top of bamboo ladders; or night-time fishing with specially trained cormorants in the Nagara river in October. One of the most famous events is the winter Sapporo Snow festival. But if you're looking for a poignant reminder of 20th century history, you could visit Hiroshima for August's Peace Ceremony.
Japan has 22 international airports and most major airlines fly to at least Tokyo and Osaka(gateway to Kyoto). If you're coming from the UK you may have to handle a stopover on an already long trip in the case of the latter, although the country's national line, Japan Air, flies direct.