[WanderingKnight]

If she really needs some sort of connection to the usual American way of doing series, you could give Cowboy Bebop a try. Its episodic style will probably attract a casual watcher much more than a regular series which needs you to focus on the storyline and pay lots of attention to it. Granted, Cowboy Bebop's style is not very anime-ish, but it's anime after all. It's not very deep in the mystery element, but it's very enjoyable nonetheless.