Dazed and Confused (dir. Richard Linklater, 1993) is a film rather than a book, but it captures pre-tech Austin better than almost any written account — the one that made the moonlight tower famous and cemented Linklater's Austin-as-state-of-mind sensibility.
The Gay Place by Billy Lee Brammer (1961) is a novel about Texas politics in the late 1950s, set in a thinly fictionalised Austin with a governor clearly modelled on Lyndon Johnson. Brammer was Johnson's aide and the novel was scandalous at publication; it is now considered one of the great Texas novels, and its portrait of Capitol-culture Austin is irreplaceable.
Lonesome Dove by Larry McMurtry (1985) is not set in Austin — it follows a cattle drive from South Texas to Montana — but it is the definitive Texas novel and reading it before a visit to Texas changes how you see the landscape. McMurtry grew up in Archer City, northwest of Fort Worth, and his Texas is both specific and universal.
The Raven by Marquis James (1929), a biography of Sam Houston, tells the story of one of the most extraordinary American political figures of the 19th century — hero of San Jacinto, president of the Republic of Texas, governor of two states, expelled from the mansion you can visit on Colorado Street for refusing to join the Confederacy.