Going to fully agree on Banana Yoshimoto, Sayaka Murata, No Longer Human, In the Miso Soup, and Out. Hiromi Kawakami's Manazuru would also be my 100 percent essential requirement, read it at home and then read it on the Manazuru Peninsula and lost my mind just a little bit.

I Am A Cat - Soseki Natsume is an older one I've been meaning to read for a while. Friend of mine loved it. A few other more contemporary Japanese Authors I like- Kobo Abe Sayaka Murata Banana Yoshimoto Izumi Suzuki Yoko Ogawa Mieko Kawakami I haven't read but heard good things about her

No Longer Human (Dazai) Out (Kirino) Naomi (Tanizaki) Norwegian Wood (Murakami) In the Miso Soup (the other Murakami) - honestly don't love this one but it's interesting for being more contemporary and focused on tourism

Since you asked for recs — Grass For My Pillow (1966), by Saiichi Maruya. A fascinating novel dealing with war guilt and postwar identity. Also something by Kobo Abe and Kenzaburo Oe, maybe "Nip the Buds, Shoot the Kids" for the latter.