The Knight in the Panther's Skin by Shota Rustaveli (12th century) — Georgia's national epic poem, written during the reign of Queen Tamara. Essential background for understanding Georgian culture and the pride Georgians take in their medieval golden age.
Bread and Ashes: A Walk Through the Mountains of Georgia by Tony Anderson — A traveller's account of walking through Georgia's mountain regions in the post-Soviet era. Personal, well-observed, and still relevant for the country's character even if some of the political details have moved on.
The Crossing Place: A Journey Among the Armenians by Philip Marsden — Covers Armenia primarily but travels through the South Caucasus broadly, including Georgia. Good regional context.
Young Stalin by Simon Sebag Montefiore — Stalin was born in Gori, Georgia. This biography covers his formative years in the Caucasus with vivid detail and is the best preparation for a visit to the Stalin Museum in Gori (which remains open and is worth seeing).
Georgia: A Sovereign Country of the Caucasus by Roger Rosen — A solid general introduction to the country: history, culture, geography. Getting dated but still a useful overview before visiting.