The Luminaries by Eleanor Catton (2013) is the most celebrated novel associated with Canterbury, though it is set in the 1860s goldfields of Hokitika on the West Coast, not in Christchurch itself. Its twelve-part structure mirrors the signs of the zodiac, its plot involves murder and opium and gold, and it won the Booker Prize when Catton was twenty-eight. It is the most ambitious New Zealand novel of recent decades and a good companion for a South Island trip. The TranzAlpine train will take you in the direction of Hokitika.
The Bone People by Keri Hulme (1984) is the other essential New Zealand novel, set further down the South Island coast at Okarito. It won the Booker Prize in 1985 and deals with violence, isolation, love, and Māori identity in ways that were and remain uncomfortable and original. It has nothing directly to do with Christchurch, but it has everything to do with what the South Island feels like — the coast, the weather, the distance, the particular quality of New Zealand alone-ness.
Once in a House on Fire by Andrea Ashworth (1998) has no New Zealand connection whatsoever, but for earthquake recovery reading, the literature that comes closest is local journalism. The Press newspaper's earthquake coverage, much of it archived online, is essential for understanding what the city went through. The Urban Dream Brokerage and Gap Filler have also published documentation of the transitional city in print.
Aftershocks: New Writing from and about Christchurch edited by various (multiple editions since 2011) collects fiction, poetry, and essays by Canterbury writers responding to the earthquake and its aftermath. Uneven in places, as anthologies are, but indispensable for understanding how the city processed what happened to it.