I am a Sydneysider, and have a couple of suggestions. Because it is August, it will be midwinter, so a dip in Bondi Beach would not be advised, however, a wander along our most famous strip of sand would still be worth it. You can do a tour of the Opera House without actually waiting for an opera to happen, too.

Taronga Zoo is world-class, and well worth a visit, and it is only a quick ferry trip over the Harbour. Darling Harbour has a couple of museum-type attractions, Sydney Tower shows Sydney from quite a different perspective, and Katoomba will be pretty at that time of year; it is about 90 minutes west of the city.