Here is a list of mangas that should appeal to old farts like me, who are too old to find fun in shonen characters getting stronger, cliché fantasy or in vanilla school romance tropes.
The main drive is that the manga should have some personality, with decent and properly written characters, laid-back humor, an interesting context and / or a subtle story. Good art and page layout are also appreciated. No violence porn or excessive fan service either, I like authors to focus on something else than these simple devices, although I'm not against them at very small doses when they serve the story. The manga may have been adapted in anime or not, I only address the mangas here.
There are probably some spoilers in my comments so skip them if you're worried about that.