That's really cool you're doing that with your daughter! Thanks for asking this too, there are good lists here.
I always recommend Mushi-shi because it's the least problematic anime I've ever seen lol. Very touching stories of people dealing with weird little spirit things and a guy that helps them out.
That has been recommended multiple times. It's already on the list but this just confirms it's ok I think.
Age appropriate I'd also suggest
Also, Link Click. Just the first season. Chinese 'time'??? travel donghua about two young men who can travel into photographs and use it to solve mysteries and personal troubles of people who come to the photography shop
Wolf Children the movie is also a really touching coming-of-age story about a pair of twins making their own way in the world. Mamoru Hosodas stuff is often overlooked for the more showy Makoto Shinkai stuff and GOAT Miyazaki, but other users in this thread have already suggested summer wars so if she likes it, she's very likely to enjoy his other stuff
I for one shall never forget Wolf Children's Lofi Hip Hop Chill Gaming / Study Beats
Summer Wars sounds like something she might like. It has been recommended a few times there must be a reason for it.
Link Click is great! Forgot I watched this recently and was so pleasantly surprised
I already saw Delicious In Dungeon (Dungeon Meshi) mentioned, so how about I Parry Everything? It's a parody of shonen tropes where the protagonist is basically just a wholesome himbo (in a D&D-inspired fantasy setting) who doesn't realize at any point in the story that he has the strength of a freaking demigod. Antics ensue.
Shinsekai yori is my favorite anime and I would consider it leftist too! There are some mentions of SA though so fair warning
I really inly warxh Gundam and Nichijou and dont know much about anime but id recommend Nichijou to anyone. It's...an absurdist sketch show with a storyline...tough one to describe without watching cause its really got its own thing going on. Its really funny and super wholesome
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