Hello everyone!

I'm looking for manga where the female lead is heart broken. Be it she couldn't get the guy she likes, he cheated on her, loneliness, long distance, etc.

I would most definitely prefer josei or something mature, targeted for older female, but any genre is fine.

Thank you for you time.

Could try the Heartbroken category. Not a lot in there, though.

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世界のどこかに 必ず
キミの居場所が ある筈

Cappuccino?

In a sense... Kimi wa Pet (at least, in the beginning...)

I specifically remember a scene like this in Cat Street where the girl breaks down about a boy.
One of the side characters in Kare Kano falls for the main lead boy. There's actually a surprising amount dedicated to her, haha.
My heart broke in the Princess Tutu anime, though I think the main characters' did too a few times, haha.

These are mostly shoujo (maybe all are shoujo?), but I still think a more mature audience could enjoy them.