Air travel - 3 weeks trip from Zurich to Japan and South Korea - Travel Stack Exchange. I will add to downhand's answer, which I mostly endorse (especially the part about the ferry!)
I will give some alternative suggestions about some of my favorite places off the beaten track, especially if you like walking. I would personally spend somewhat less time in Tokyo and Seoul -- they are delightful places both, but in my opinion the tourist sights in both places can be missed. A Beginner's Guide to Cherry Blossom Viewing: When do the cherry blossoms bloom?
When do they bloom?
The most important factor in determining the blooming time of cherry trees is the geographical location. Generally, the milder the climate, the earlier the blossoms open. On Japan's southern, subtropical islands of Okinawa, cherry blossoms open as early as January, while on the northern island of Hokkaido, they bloom as late as May. In most major cities in between, including Tokyo, Kyoto and Osaka, the cherry blossom season typically takes place in early April. Furthermore, the blooming time of cherry trees differs from year to year depending on the weather.
Fashion. Food. Hotels. Kyoto. Language. Money. Tokyo. Transport.