I second Ando Lloyd.
I would also suggest : Nazo no Tenkousei (more scifi), Atami no sousakan (hard to describe), Death note (fantastic), Youkai Ningen Bem (fantastic), Long love letter (fantastic/scifi), Oniichan gacha (fantasy), Shinigami-kun (fantastic?), SPEC (fantasy?), Toki wo kakaeru shoujo (fantastic), Tokio (fantastic), Yamada-ku to 7-nin no majo (fantasy), and others... There is also the currently airing Repeat (fantastic).
All are Japanese, I don't think there is the kind of japanese girls you dislike, there are few romances though. Japan has a lot of fantastic/fantasy movies too.
As much as I love Quartet, I don't see how it could be labelled as a fantastic drama...