Been reading it lately, and it helps reduce my scrolling time. I've hardly read any, so you can recommend really popular stuff, too.
I've read Vagabond, 20th Century Boys, Claymore (years ago), and some berserk. I just finished reading Teppu, which I thought was an interesting subversion of a lot of anime tropes. I also liked that it was a short run (only 8 volumes). I guess I like seinen, but I've also enjoyed josei like She Loves to Cook, and She Loves to Eat.
Anyway, no shonen please. Hard mode: please nothing about high school
A few of these are from shonen magazines, and a few have high school age characters in them, but I don't think they break your requirements in spirit.
Boku no Mura no Hanashi — As far as I can tell, there's only one volume available in English, and it's only available online. It's a fictionalized retelling of the Sanrizuka Struggle which is an important chapter in the history of the modern Japanese Left.
Yokohama Kaidashi Kikou — This is a chef d'oeuvre of gynoid fiction and the most relaxing depiction of the middle of mankind's extinction I know of. I strongly recommend it. It's about a robot girl called Alpha who runs a quiet countryside café near a Yokohama which has been submerged underwater. Alpha takes photos, she has human friends and a robot friend, she plays music on her moon guitar and awaits her owner's return.
Non Non Biyori — This is about the lives of four kids in a small farming community in the middle of nowhere: a first-grader, a new kid, and two sisters; and there's also a fifth kid but he never talks. Sometimes the chapters focus instead on the grown-ups around these kids. The anime adaptation of Non Non Biyori is great as well and if you've seen it you won't mind re-experiencing it in manga form.
Akane-banashi — The main character Akane's dad failed a rakugo test and basically gave up on his dreams of becoming a rakugoka after that, and so Akane is sort of trying to avenge him by becoming a rakugoka herself, and she dedicates her all to it and kicks ass. It's top tier.
A Bride's Story — It takes place in 19th century Central Asia. I just think that's cool.
My Journey to Her — Autobiographical manga by a Japanese trans woman. I guess it's been translated into English since I last read it myself, judging from the fact that it suddenly has an English title on Anilist, when it used to be called "Boku ga Watashi ni Naru Tame ni". A positive note is that since this manga was first published, some of the information in it has become dated due to progress in trans rights in Japan.
Yotsuba&! — This one is an absolute classic. The main character is a five year old girl adopted from a non-specific foreign country by a single dad, and the manga is basically just this kid's random adventures. It's the number one most recommended manga for learning Japanese. I guess you can say that Yotsuba&! is kind of like urban Non Non Biyori in a sense.
Aria — This one pairs famously well with Yokohama Kaidashi Kikou because it's in a similar vein of relaxing manga depicting a future which, for all its new technology, is still pretty "rustic". Aria is about a terraformed and renamed Mars far off into the future, where a 1:1 replica of Venice has been built, and the main characters are all gondolier tour guides. It's really imaginative and optimistic. Note however that Aria was originally called Aqua.