Let me suggest another alternative. Shikoku. Fly into Kansai International (KIX) and train from there via Shin-Osaka and Okayama.

Takamatsu has one of the 3 most highly regarded Japanese gardens in Ritsurin Koen and the nearby ropeway takes you to a wonderful viewpoint out over the Inland Sea. Matsuyama has the famous Dogo Onsen hot spring which was the inspiration for the onsen setting in the Academy Award winning "Spirited Away" animated feature by Hayao Miyazaki, although it has gotten a bit dumpy and I wouldn't recommend actually using it. And Kochi, located in a near sub-tropical setting on the Pacific Coast (the climate reminds me a bit of San Diego) has an historic castle and monuments and museums dedicated to major historical figures instrumental in the early shogunate and the later fight for restoration of the emperor and overthrow of the shogunate 265 years later. Several of the famous temples on the also-famous 88-temple Shikoku pilgrimage are easily reachable from the major cities without actually hiking any of the pilgrimage. The train ride down to Kochi from Okayama, Takamatsu or Matsuyama is a spectacular trip through a rugged mountain gorge that is worth the trip by itself.

If you have a day or two left at the end, stop over in Okayama on the way back to visit the second of the three "best" gardens in Japan, Kora-kuen, and the nearby "Black Crow" feudal era castle. Depending on what time your flight home leaves, you can easily leave from Okayama on the day of return home. I did it the last time I was there as my flight was in late afternoon.

Shikoku in late March will be glorious as will Kora-kuen.