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The closests mountains from you would be Perisher and Thredbo which I really can't comment on because I haven't been to either.
Then you can check out the Victorian mountains such as:
Mt Buller: In my oppinion this resort has the best night life out of the three. 3 Parks which are moderate in size and features are generaly good but not fantastic, though there dependent on weather conditions, snow.etc. A bit of skiable terain has a few mellow bowls and some nice chutes and lines.
Mt Hotham: Pretty average resort, I think it has 2 terrain parks which are poor to average. Allright night life, more skiable terrain then Buller though.
Falls Creek: Probably the best resort out of the three, when they have the park at ruined castle open it has to be one of the best parks in Australia following perisher or thredbo. Pretty good night life. And it has a lot of natural terrain.
That's just a run down on the Victorian resorts and this is my personal oppinion you can take with a grain of salt if you like, but I'm sure there are many more Australian ns'ers out here to help you with the following topic. But your best bet is to go to Perisher or Thredbo and if you have enough cash head over to New Zealand, I would reccomend Wanaka would be the best spot to go cause you've got Cardona, Treble Cone, Snow Park along with a lot more resorts.
Hope this Helps.
all resorts are a relatively long way from any main city (apart from canberra, which is half a day from sydney??(correct me if wrong on this, im from brisbane ay).
from canberra slopes are 2 hours drive where you'll find the two major australian resorts perisher and thredbo. resorts are nothing like overseas as you'd expect. wont find too many challenging runs, parks are generally well maintained but all depend on the amount of snow that's been dropped.
But yeah Perisher and Thredbo are your best bets, just watch out for ticket and accomodation prices theyre pretty steep.