The Secret River by Kate Grenville (2005) follows a convict family who settle on the Hawkesbury River north of Sydney in the early 19th century. It is not about Katoomba specifically, but it gives the most searching fictional account of the colonial encounter with the Australian bush — the landscape, the fear, and the violence — that shaped the country around which the Blue Mountains sit. Essential background reading.
True History of the Kelly Gang by Peter Carey (2000) is set in Victoria rather than New South Wales, but Carey's rendering of the Australian bush as both refuge and trap, and his ear for colonial Australian speech, captures something true about the interior landscape. If you are driving west from Sydney and the bush closes in around you, Carey's voice returns.
Eucalyptus by Murray Bail (1998) is set on a fictional Australian property where a man agrees to give his daughter in marriage to whoever can name every eucalyptus tree on his land. It is a strange, beautiful novel about the Australian landscape, its specific tree-names and the stories that grow around them — useful preparation for a place where the eucalyptus forest defines everything you see.
The Blue Mountains: A Cultural History by Greg Mackay is a solid introduction to the history of the mountains — the Aboriginal peoples, the early explorers who crossed the ranges in 1813, the Victorian resort era, and the conservation battles that eventually secured World Heritage listing for the national park. Not a novel, but the clearest narrative account of how the mountains became what they are.