Are you interested in more modern books or older ones? Many Japanese novels seem odd compared to our culture. They approach responsibility and adversity differently, and suicide is also seen much differently. Goodbye Tsugumi is interesting, by Banana Yoshimoto. Two cousins who have grown up together, one seems like a dark character, but the other sees her with an understanding perspective. An older, very beautiful book is Snow Country by Yasunari Kawabata. The imagery is very good. The Woman in the Dunes by Kobo Abe is a bit chilling and creepy but also interesting....Murakami was my first Japanese author, and I've read quite a few of his books now. I started the first page of that first book full of anticipation about learning about the Japanese culture, and the protagonist at the start is cooking Spaghetti Bolognese and listening to the Beatles!
I also read The Bonsai Tree by Meira Chand when I was a teenager - the author was Swiss Japanese and writing about a Westerner marrying a Japanese and discovering some down sides to the culture, not just the up. It was very good and I ended up reading another by her that was set in China.
If you've got some Japanese-author books to recommend, we're both interested in sampling more!