Spend a day reading among walls of manga
Manga are Japanese comics, and at these museums tens of thousands of volumes line the walls, free to take down and read inside. Pick up a classic or a series you have never heard of, and read for as long as you like. Most books are in Japanese, but the pictures carry much of the story, so you can enjoy them without reading every word.
A manga museum in a former elementary school in central Kyoto, where a "wall of manga" of about 50,000 volumes runs through three floors. Take any volume off the shelf and read it on a bench or by a window for as long as you like. It is next to Karasuma-Oike subway station, and most of the books are in Japanese.
A manga museum in a building right in front of Kokura Station, with a reading zone of about 70,000 volumes that you can read freely inside. Its exhibits celebrate manga artists linked to the city, including Leiji Matsumoto, creator of the space adventure Galaxy Express 999. Kokura is about 15 minutes from Hakata in Fukuoka by bullet train.
An art museum in Akita Prefecture, in northern Japan, that keeps a large collection of original hand-drawn manga pages, and its permanent exhibition is free. After seeing the drawings, go to the manga library upstairs and read the works you just saw. It is far from Tokyo, so it fits best into a trip around northern Japan.