Maison Ikkoku is a romantic comedy anime series by Rumiko Takahaski (Ranma, Inuyaha, Urusei Yatsura). Tells a very mature love story about a young widow and a college student. It captures life in 1980s Japan very well. Very different than what has been listed thus far, but it gets high praise by the vast majority of reviewers. If your girl is into anime, you should definitely recommend it to her.