Well, I'm not going to be parochial. The skies in Wollongong are awful. It travel about 45 mins to observe in the southern highlands. Even there the skies are not as good as they used to be in Wollongong in the 70's. A bit further afield and things improve considerably - I've seen great skies at Bungonia and around Goulburn - but for one night trips the travel time gets prohibative.
IMHO you should look at Perth as an option. Being relatively small it's easy to get out of town and the air is very stable and dust-free because it has just come off the Indian Ocean. I've seen the Horse Head in a 20cm newt from Dryandra (where ASWA have their astro-camp). But I think the skies up on the Yilgan Block around Leonora and Meekatharra may be better (I didn't have a scope so that is a naked-eye estimate). Even a site up in the hills above Perth, still in suburbia, used to be good. That was >20 years ago so things may have changed for the worse.
BTW the area around Meekatharra and also the northern Flinders Ranges were on the short list of locations to site the 3.9m AAT, which was eventually placed at Coonabarrabran. As I understand the main advantage of Coonabarrabran was that it is closer to the main population centres (especially Sydney and Canberra) where the astronomers work. This was, of course, in the days when astronomers actually had to travel to an observatory to do obs.
If you do decide on Sydney (and I assume the same is true of other cities) think about where in the city you want to live. It can easily take an hour to cross Sydney. So, if you were to leave from Bondi by the time you got to Liverpool someone who left Liverpool at the same time would be most of the way to Goulburn. Then again, only a madman or a masochist would live at Liverpool if they worked at Bondi.
Happy debating!
