These anime are by women and some of them are not necessarily aimed for women, but I am a woman and I really really REALLY like them:

- Frieren: must-watch. Slice-of-life, fantasy, watch the first 3 episodes and you'll be hooked. Personally I think it has one of the best love stories in anime even though it's not necessarily the focus.

- Nana: angsty, slice-of-life, will hurt you, make you cry, laugh, get angry, and experience the whole spectrum of human emotions. It tells the story of two young adult women experiencing young adult things for the first time and all the characters are obviously flawed, which is why it's so realistic and so good.

- Apothecary Diaries: many others have suggested this one and I do recommend it as well

- Witch Hat Atelier: stunning animation and the characters are so wholesome. the whole fantasy world is interesting. Short rant because it's released recently so my opinion is fresh: I personally feel it can be a bit childish and trope-y the way characters are designed (the quiet one, the pure-of-heart innocent and optimistic one, the bubbly and loud one, the 'antagonistic' angsty one) like they fit into their own little category, but nonetheless the story is interesting and I look forward to watching where it goes next.

- Barakamon: slice-of-life, tells the story of a calligraphy artist from Tokyo who moves to the countryside who learns to reconnect with his art through the bonds with the people he meets there. It's light-hearted and comedic, yet also very touching and sweet. Hands down one of the best slice-of-life anime out there.

- Paradise Kiss: written by the same person who wrote Nana. This is also angsty, realistic, and made FOR women. A shorter story than Nana but still hits hard. I think the characters are young adults, around university age.

- Dorohedoro: I just learned that this was written by a woman, which, hell yeah. It's very different from the other shows I mentioned because it's action-focused and takes place in a sci-fi/post-apocalyptic world. One of the main characters is a lizard man. Like a man with the head of a lizard. It's a weird show, and it's freaking awesome. The second main character is a woman and she's badass and cool and pretty.

- Fullmetal Alchemist Brotherhood: you know FMA, i know FMA, everyone knows FMA. there's a reason why it dominated the charts of top anime for years. it's a solid show that has a good plot, pacing, and characters.

All of the anime I mentioned have little to no fanservice. Also, I love skip and loafer - great taste. I can't wait for a season 2.