We took the bus from Saint Ignatius’ College, Riverview, having decided to walk across the Sydney Harbour Bridge. (We were not tempted to do the bridge climb 134 metres above sea level which is a different experience altogether and costs from Au$248 http://www.bridgeclimb.com/#your-arrival).
Heading through the Burton Street Tunnel (Markets are hosted in here every 2nd Sunday of the month), you will see signs to Cahill Walk/Harbour Bridge follow these. You will reach a set of stairs leading to the bridge
Continue along the path until you would see another sign pointing to the Botanic Gardens, that part of the pathway affords great views looking down onto Circular Quay, following the Cahill Expressway, including both Opera House and Harbour Bridge, but we went down towards the rocks and then made our way home from the City Centre.