Moore Park next to a residential area just outside of Sydney CBD, where you can camp in your car. As always, please don’t disturb the neighbours. There is drinking water available, however, no showers. to shower you will need to go to one of Sydneys beaches.
A great thing of this spot is, that there is a bus station literally right next to it. From here it’s easy to get to the city center or to Bondi by bus. If you don’t mind you can also walk to all attractions in downtown Sydney without any problem.
You are actually not allowed to leave your car here longer than 4 hours, however, it is very unlikely that you will be checked, just move it every now and than. The name of the street is Robertson Road, leave your car at the end of it (the bus station is just outside at the main road).