Sydney Harbour Bridge
Spanning the harbour, the Sydney Harbour Bridge is one of the city's most imposing structures. You can walk across it on the Opera House side (the other side is for trains and also has a cycle-way). You can drive across it; there is an e-tag toll one way (into the city). Drivers not wanting the scenic route can use the under-harbour tunnel. You can visit the Pylon Lookout in the South-East Pylon which houses an exhibition on the construction of the Sydney Harbour Bridge and, some 200 stairs up, there's an observation deck with excellent views of the city and harbour. The Pylons are purely cosmetic. They were built to give the bridge a more powerful look. The Pylons were actually built after the completion of the arches and it would be an ordinary looking bridge without them. The iconic structure turned 80 in 2012.
As mentioned, you can climb it. BridgeClimb, despite its price tag, is arguably Sydney's best attraction if you are up for the challenge. While not for those with extreme vertigo, it is completely safe. You receive training before the climb and at all times are attached to the bridge with specially designed harnesses to take you 134m above the harbour. You will also be breath-tested before being allowed to take the climb. If there's a positive reading, climbers are given a second test and, if over the limit, will be rescheduled to a later climb. You only need a moderate level of fitness - it's informative, exciting and the view is terrific. There are Night Climbs as well and a 'Discovery Climb, which takes you along the suspension arch with lots of weaving and fantastic views. As well as purchasing a thrill and a view, you will have bought a lifetime memory.