The Tale of Genji is regarded as one of Japan's most prized national treasure, which is to be extected, since it is also thought to be the first novel ever written. It was written by a woman, under the pseudonym Murasaki Shikibu, of the Japanese court around the mid-late 10th century, at a time when fictional was considered uncouth and unndignified, and when women were considered more or less the properties of men and should stay in the kitchen etc.
It stars a prince, by the name of Genji. He is the beauty of the world but cannot be made emperor because hsi father had him from a servant woman who he loved, instead of his wife.
In full, it is Bible-long. More than one thousand pages. I have this edition, which includes the majority of the first 17 chapters: http://www.amazon.com/The-Tale-Genji-Penguin-Classics/dp/0143039490

I've found a website of free novels for girls. I know you like TV dramas about school life and teenagers ;-)  This offers short stories written in colloquial language.

http://novel.maho.jp/youth/

Hope you enjoy!

Personally, I like Shusaku Endo's serious novels, Miyuki Miyabe's and Asa Nonami's misteries.

Jordan, you know about the Tale of Genji! I have read its manga style novel called Asaki Yumemishi. It's much easier to try :)

Elias, it's actually Wagahai wa Neko de Aru, not watashi. It's the reason I refuse to read it in English. :) Wagahai is very self important, used by noblemen and such. That sort of nuance is lost in English. 

Anyway, for Kiki. I'm trying to think of good books I've read about Japanese culture but I can't seem to think about any. Most modern literature references The Tale of Genji, which gives pretty in depth descriptions of classical Japanese court culture but it's very long. Also, I don't think it's the most entertaining book I've ever read. 

I'm generally a fan of Natsume Soseki, but he's not modern so if you're looking for stuff with today's culture you won't find too much. I once read an entertaining short story about Natsume Soseki and Sherlock Holmes, since he had studied in London during that period. 

While in college I had to read a book called Japanese Culture that I actually found quite interesting. It wasn't literature, so there was no story to keep you entertained but it gave a great overview of Japanese history, art, and culture. I believe it's in that book that I actually learned the origin of kamikaze. 

Depends what you're looking for. From what I've read, it seems that if you want a book with very vivid descriptions of Japan and Japanese culture, it's best to read a foreign author rather than Japanese, because they don't assume you've any understanding at all of the Japanese culture and provide great detail for architecture, ceremonies, etc:

If you're looking for that, James Clavell's "Shogun" is an amazing novel based around feudal Japan of 1600 thereabouts. Excellent overview of classic Japanese sensibility, the strange 'hostage' economics, and bushido, tea ceremony, and just so much more.

And it's an excellent work of fiction too! Very touching, gripping story.

Likewise with classic Japan, Eiji Yoshikawa's 5-book 'Musashi' series is also excellent. It does seem like the translator took a bit of leeway with description, as the book, in English, reads much more like a western author's novel than it does a Japanese--- which is a good thing, in my opinion, particularly because of what I said above.

It chronicles the life of the ronin Musashi, who is argued the great swordsmen who ever lived, and the story is simply excellent.

Also, you can't go wrong grabbing the 2 editions of 'Traditional Japanese Literature' by Haruo Shirane. Undoubtedly the most comprehensive and ambitious collections of classic Japanese literature all the way from the very beginninings of the 'nihon shoki' through post-Edo period, both collections offer an outstanding range of Noh plays, folklore, puppet stories, ghost stories, mythology, and just about everything.

You can read Watashwa Neko de aru, written by Natsume Soseki. It describes the Japan of just after the Meiji revolution

Or even better , Basho's Oku no hosomichi