I already implied this, but... First impressions are critical.
If I were you, I would hold out for an (all-ages-acceptable) masterpiece like like
Mononoke Hime or
Seirei no Moribito. After all, you will be interested in anime for years to come; thus you have no time pressure. So why not wait to show her something until she capitulates on the 'must be mystery' term? As for Mononoke Hime, I'm sure most people who are skeptical about anime would rather watch a movie of random genre than an entire season of a specified genre. On the other hand... my mom fell asleep when I tried to show her Mononke Hime. This was in the middle of the day, with daylight streaming in the windows, with 6 other people present
But on the other hand, my mom also fell asleep during Star Wars in an actual theater. At any rate... I think if a person is determined to remain dismissive toward something, then they will, no matter what. But if they might actually accept something, it is your responsibility to present them with
the best possible chance, regardless of random uninformed demands they might make.
P.S. As for Monster - if it was well-executed for its entire duration, I would recommend it, despite the length. But... it isn't
There are also possibilities like Gakuen Alice and Card Captor Sakura. But, of course, the characters are all children. So on a
superficial level they appeal to children... but if you have not seen them, I highly recommend that you do, because they are very good - much like
Twinkle Twinkle Little Star, which is normally considered as "for children", yet Mozart found it quite intriguing.