Sydney is the capital city of the Australian state of New South Wales, and Australia's largest city. A week in Sydney will help you see many of the sights of Sydney and its surrounds, and understand the city and its culture.f you're up for exploring the area by bike (one of the best ways to do so as much of it is parkland), take the train to Concord West station on the Northern Line (red line on the Sydney Trains map-about 20-25 minutes from the city on a direct train).