While I don’t necessarily have specific recommendations, you might want to check out 小説家になろう, a website where japanese people post books they write for general consumption (including all kinds of genres, it’s not all 異世界).
You might have a look at the rankings for the genre you’re interested in to see what’s popular (and therefore hopefully good).
cracks knuckles (though I should say up front that I’ve only ever read these in English)
Fullmetal Alchemist / 鋼の錬金術師 by Hiromu Arakawa / 荒川 弘
The Guest Cat / 猫の客 by Takashi Hiraide / 平出 隆, this very charming and strangely melancholic story about a couple and how a wandering cat changes their lives
Haruki Murakami, as mentioned, though I go seriously up and down on him. Some of his books are great, some of his books I don’t like much, and others (even some of the ones I think are great!) I would hesitate to recommend without also including a hefty warning [?!]. From what I’ve read though, you’ve straightforwardly got Hard-Boiled Wonderland and the End of the World / 世界の終りとハードボイルド・ワンダーランド, Kafka on the Shore / 海辺のカフカ [?!], After Dark / アフターダーク, and The Wind-Up Bird Chronicle / ねじまき鳥クロニクル . In the not so much pile (but possibly still worth checking out), you’ve got 1Q84 (which some people love, and left some people cold - my feelings on it veer up and down erratically across the book as a whole) [?!], Norwegian Wood / ノルウェイの森, Hear the Wind Sing / 風の歌を聴け (which is solid enough slice-of-lifey kinda stuff), and Colorless Tsukuru Tazaki and His Years of Pilgrimage / 色彩を持たない多崎つくると、彼の巡礼の年 [?!]
In the Miso Soup / イン ザ・ミソスープ by Ryu Murakami / 村上 龍
Red Girls: The Legend of the Akakuchibas / 赤朽葉家の伝説 by Kazuki Sakaraba / 桜庭 一樹, this sort of sweeping social history of 20th Century Japan, interlaced with supernatural-type elements
Cells at Work! / はたらく細胞 by Akane Shimizu / 清水 茜, this adorable and occasionally absurdly violent manga about anthropomorphized cells in a city that represents the human body, going about their normal tasks of keeping it functioning (though now I think about it this would have pretty specialized vocab, wouldn’t it)
Well, other than things already recommended, there’s 万能鑑定士Q. It’s interesting enough; I wouldn’t say it’s the best ever though. It’s a series, so it might get better in later volumes, not sure. In any case, it’s wordlist is available on floflo.moe (an SRS website for learning vocab from books), which is a plus.
舟を編む (The Great Passage, a drama about a team of people making a new definitive dictionary of Japanese language. Available in english translation; also as anime and as live-action drama, with English subtitles). I’ve linked to Kindle edition at Amazon Japan; I prefer Kindle books because I can get them immediately (I live in USA), and because it’s so easy to look words up in the dictionary.