Take a ferry to Taronga Zoo wharf and then head to your right along the promontory. There's pristine bushland (almost unchanged from the time of European colonisation), quiet beaches, and knockout views across the harbour, and in the warmer months you'll spot plenty of Eastern Water Dragons, a type of large lizard. Once you reach the tip of the headland, you can either amble back to the wharf or - if you're feeling more ambitious - follow the track several more kilometres to Clifton Gardens, ogling the gigantic houses along the way. From there, you can either hike all the way back to Taronga or get a bus to a ferry wharf.