After an adventurous drive with our rental car through the city center to our hotel, which is mostly blocked due to a construction site, we then looked for a gas station. With Google, we drove through the traffic - unfortunately, the gas station displayed there did not exist. After wandering through the city with the GPS signal repeatedly dropping, we finally found a gas station and were able to return the car fully fueled at the rental car station.
We were glad to be able to get around without a car and walked through Hyde Park to the city center. There we saw the oldest surviving cathedral in Australia, St. Andrew's Cathedral.