Botchan by Natsume Soseki (1906). The short, comic novel that made Matsuyama famous in Japanese literature. A brash young Tokyo teacher is sent to a provincial school in what is clearly Matsuyama, and spends the whole book complaining about the narrow-mindedness of the locals. Sharp and funny, and gives a vivid sense of Meiji-era Japan seen from the inside.
Saka no Ue no Kumo (Clouds Above the Hill) by Ryotaro Shiba. A massive historical novel following three men from Matsuyama through the Meiji era into the Russo-Japanese War — the era that transformed Japan from feudal isolation to modern state. The dedicated museum in the city is built around this book. Only partially translated into English, but the museum explains the story well.
The Narrow Road to the Deep North and Other Travel Sketches by Matsuo Basho. Not directly about Matsuyama, but Basho's influence on the haiku tradition that Masaoka Shiki later reformed is impossible to separate from this city's literary identity. Reading Basho before visiting Matsuyama gives context for why Shiki's revolution was so significant.