Akira - a cinematic masterpiece that can be a bit confusing the first time through but any fights that are in it or explosions all have a purpose and in some cases push the story forward.

Angels Egg - If you’re a fan of the Dark Souls/Bloodbourne/Elden Ring games then you might as well view the film that inspired it all. This one WILL make you think. and regardless of its inspiration for those games there are no fights or anything like that. It sets the mood. Very gothic-dystopian.

Bocchi the Rock! - An anime about a girl with massive social anxiety and her joining a rock band. it’s funny, the music is awesome, and if you have any sort of anxiety it’s relatable.

FLCL - A stylized weird tale of a boy with a robot in his head and everyone, except himself, want him to live up to his brothers reputation (and that’s just being incredibly basic with the plot) great music, awesome art style.

Paranoia Agent - A mysterious kid with a baseball bat goes on a serial assault spree in Tokyo. His actions affect many people, all of whom you’ll learn about and follow, and how they could potentially be connected to each other and even the kid. Great mystery tale that REALLY makes you think. I personally love this one.

Cowboy Bebop - Yes there are fights, yes there are explosions, but this one is honestly an absolute classic that is worth the watch with by far the best anime soundtrack ever. Fantastic story with amazing characters that you’ll instantly connect with. you WILL care about these characters and by the time you hit the end you WILL be emotionally invested in the crew of the Bebop.

DoroheDoro - dude with a lizard head is trying to find his real head. There are some fights in this but it’s damn great and really funny. On my first watch through I loved it so much I immediately watched it through again. Characters are great and the style/music are awesome.

Deathnote - It’s silly in the way it pretends to be incredibly serious. You’ve probably seen the countless memes of this show but at it’s core it’s a goofy anime that is a sort of satire for all the incredibly serious anime. Just the way they will explain the plot or things in the show you just have to roll your eyes and laugh.

One Punch Man - again, you don’t want a lot of fights but again this is a satire of all the “super hero super power” animes like Dragon Ball Z. Random nobody salary man decides he wants to be a super hero…over does it a bit.

Finally my personal favorite anime/series of all time which might not be up your ally but it has influenced and inspired so many things like the Matrix films, Countless movies, tv shows, other anime, videogames, cyberpunk in general…

Ghost in the Shell the movie - series Stand Alone Complex and S.A.C 2nd Gig

GitS is my absolute favourite anime series of all time. I watch it back constantly. just fantastic stories, setting, and various plots that questions are we even human anymore? what differentiates us from machine? The film Ghost in the Shell is a cinematic masterpiece and just watching it you’ll see scenes and think to yourself “I’ve seen this before” because you probably have but not from the film itself. You’ve seen this in films, tv, videogames, comics, other anime that have pulled scenes and pieces FROM Ghost in the Shell and adapted it to whatever they’re making.

There are other series I really enjoy like Fire Force but I don’t think that one would be for you. lots of fighting, LOTS of explosions and LOTS of a fan service but it’s funny and I enjoyed it.