I think a better bet would be an animated movie, since they're shorter and if she doesn't like it, she'd still have watched it completely (which avoids the whole ''no this anime only gets good after 200 episodes'' debacle). 

Kotonoha no Niwa (get past the weird, by Western standards, storyline and focus on the art and storytelling and you'll be fine) is a good one. "Your Name" is OK and throws a kinda weird plot twist at you which could be considered 'dramatic' question mark?