Anime fans, help!

So, if you were looking for anime series appropriate for a twelve-year-old, what would you suggest?

The girl in question is intelligent and relatively mature, but her parents are both careful to make sure she doesn't get exposed to inappropriate stuff.

I started off with a recommendation for most of Hayao Miyazaki's work, since like Pixar his stuff is appropriate for all ages without being shallow or kiddified, and I threw in a few other suggestions too. But I've missed so much anime - it's something I tend to dip in and out of - that I can't really offer exhaustive suggestions.

Any tips? :)

(Crossposted to both journals; apologies if you see this twice!)