My personal highlight of August is city2surf run. It is one of Australia’s favorite event and even you are not runner go to cheer for participants of this 14 kilometers run from city center to Bondi beach. The run this year is on 12th of August.
Between Saturday 28 July and Monday 13 August from 06.00 to 18.00 (6am – 6 pm) Customs House Square will play host to one of the official London Games 2012 screening sites in Sydney. Live games and highlights will be shown on the super screen for 12 hours a day. Various sporting activities will also be set up on the square during the 17 day period.
Entire August 18th Biennale of Sydney is open with various performances, film screenings and other special events. Everything is FREE the public.
Check this website for full list of events in Sydney.