Canberra Airport, about 8 kilometres east of the city centre, has direct flights from all the major Australian capitals (Sydney, Melbourne, Brisbane, Adelaide, Perth, Hobart) and a single international route to Singapore. It is a modern, easy airport — security queues are short, the terminal is one building. Taxis and ride-share to the city are around AUD 30; the public bus is much cheaper.
By road, Canberra is 286 km from Sydney (about 3 hours on the Hume Highway and Federal Highway) and 660 km from Melbourne (about 7 hours). The drive from Sydney is straightforward; from Melbourne it is a long day. The coach companies (Murrays and Greyhound) run multiple daily services from both cities.
By rail, the NSW TrainLink Xplorer service runs three times a day from Sydney Central to Kingston station in about 4 hours 20 minutes — slower than the bus and slower than driving, but pleasantly scenic through the Southern Tablelands.