
I love travelling by train. It is such a hassle free option when compared to planes... Do you know that ,as a visitor (and Japanese who has lived outside Japan more than 5 years) you can buy an all inclusive train pass which allows you to travel across the country?It is called JR Pass (Japan Rail pass) and you can choose it's duration .
3 days in Tokyo (getting familiar with the culture and over the jet lag) 1 week across the country, and the rest of time in Tokyo where you can purchase tech and enjoy urban culture before returning to your home.
Of course, if you live closer to Japan or have the opportunity to travel longer, you could extend your travels around the country but the way we travel (on place per day) gets a bit exhausting. Hence, given the extra time, you could slow down in key places.
For that week , there are many possibilities... Subject to what kind of things you like doing. One thing to be mindful of is that in the past 12 years , there has been a dramatic increase in the number of tourists and hence if going to the typical places, timing will be key.
We have been to Japan in autumn a few times and generally find it to be less stressful than spring. It is true you will not see the sakura- cherry blossom- but you will the momiji -red maple/ Acer leaves