For mostly non-violent shows that are reasonably easy and aren't 'romances' (although it's almost impossible to find a show that has -no- romantic subplots, of course), try,
Non Non Biyori
Tari Tari
Kotoura-san
Nagi no Asu Kara
Polar Bear Cafe
Erin
Locodol
All these are on crunchyroll which I use a lot because I can turn subtitles off if you're a subscriber. (I guess that's starting to be true of other services too, but it didn't used to be).
Of course, most non-violent anime have a pretty strong 'cute' factor too, I don't know how much or what kind of 'cute' bothers you so, well.
Erin and Nagi no Asu Kara are set in fictional worlds, so you won't learn much about Japanese culture from them. Not that you can trust anything you learn about Japanese culture from Anime anyway. A lot of real things are reflected in Anime, but you don't know what's real and what's ... how to put this... the Japanese own stereotypes of themselves.
There is a show that animates all the mukashi-banashi, but I find it horribly dull to watch even though I enjoy reading/listening to mukashi-banashi at
福娘童話集 -世界と日本の童話・昔話集- .
Of course, folktales are not an accurate depiction of anything, but everyone in Japan knows these stories. If you know them too, you'll pick up references to them all the time in anime and cinema.