If you enjoy a nice day at the beach I recommend Manley Beach. It is a half hour ferry ride from Circular Quay (near Opera House) and has the added benefit of a beautiful harbor tour. In fact even if you don’t want to spend time on the beach, the ferry is basically a harbor tour for a much cheaper price.
When you get to Manly, don’t be fooled by the mini beaches adjacent to the Ferry terminal. You will walk a couple enjoyable blocks on The Corso and actually cross from Sydney Harbor to the Pacific Ocean.
You’ll like the ambiance, pubs, beautiful ocean and beautiful people. If you need serenity then this is not the place for you.