Sydney Observatory sits on Observatory Hill above the Rocks, with one of the best easy views over the Harbour Bridge and the western side of the harbour. The building dates from the 1850s, when it served as a working observatory, timekeeping station, and signal point for ships entering the port.
The small museum explains the site's astronomy and maritime history, and the grounds are worth visiting even if you do not go inside. It is an especially good stop with children, since the science is tangible and the hill gives them space to move around.