Nodame Cantabile is what I call a "senpai romance" where a younger woman falls for her older mentor. There are others in this genre, particularly
Toshokan Sensou,
Planetes, and perhaps
REC. In these the young lady is training to be an armed librarian, a space trash collector, and a voice actor respectively.
Along the lines of
Chihayafuru, I'll add two other shows about board games, the rather well-known
Hikaru no Go and its punningly named "sister"
Shion no Ou. They both focus on middle-schoolers who decide to pursue a career as a competitive game player, Go in Hikaru's case and Shougi ("Japanese chess") in Shion's. Hikaru's story follows the memes of shounen "levelling up" stories; Shion's includes a murder mystery as well.
Another possibility might be
Nijuu Mensou no Musume about a young girl who is kidnapped by a master thief and learns his trade.