The Uttermost Part of the Earth by E. Lucas Bridges (1948) is the essential book about Tierra del Fuego. Bridges grew up at Estancia Harberton, son of the missionary Thomas Bridges, and spent his childhood among the Yagán and Ona (Selk'nam) peoples. His memoir is an intimate, sympathetic, and irreplaceable account of those peoples and this landscape before both were radically transformed. No other book comes close for understanding what Tierra del Fuego actually was.
In Patagonia by Bruce Chatwin (1977) is the book that put Patagonia on the literary map. Chatwin doesn't spend much time in Ushuaia itself, but the obsessive, fragmented, deeply personal account of his journey through southern Argentina shaped how generations of travellers have seen the region. Worth reading for the prose alone.
The Voyage of the Beagle by Charles Darwin (1839) covers Darwin's years along the Fuegian coast in detail. His observations of the Fuegian people he encountered — and his account of the extraordinary experiment of bringing four of them to England and returning them — are part of the origin story of this place.