Fortunata and Jacinta by Benito Pérez Galdós. Galdós was born in Las Palmas in 1843 and became the greatest Spanish novelist of the 19th century — his country's answer to Balzac or Dickens. This vast double novel, set in Madrid, follows two women in love with the same man across decades of middle-class Spanish life. Galdós saw society with a clarity and sympathy that his contemporaries found uncomfortable. Starting with this one is the right call; you can visit his birthplace, the Casa-Museo Pérez Galdós in Vegueta, before or after reading it.
The Canary Islands by Noel Rochford. A thorough introduction to the archipelago's history from the first European contacts in the 14th century through conquest, colonisation, and the role the islands played as a waystation between Europe and the Americas. Covers Gran Canaria in detail, including the fate of the Guanche people whose remains you will see in the Museo Canario.
The Guanches: Survivors and their Descendants by Rafael Muñoz Jiménez and José Luis Concepción. The pre-Hispanic inhabitants of the Canaries — the Guanches on Tenerife, but also the Canarii of Gran Canaria — remain poorly understood outside academic circles. This introduction to their archaeology, burial customs, and genetic legacy gives the Museo Canario's collection real context. Not a light read, but the right preparation for the island's archaeology.
South from Granada by Gerald Brenan. Brenan's classic is set in Andalusia rather than the Canaries, but his eye for Spanish provincial life — the pace, the politics, the pleasures — translates directly to the feel of Las Palmas. Read it for the same reason you'd read Laurie Lee: for a tone of voice about Spain that still rings true.