Mate,
I'd be steering clear of Bankstown, you'll get ripped off, they'll want you to 'checkout' on Bankstown's Class D procedures before they let you loose. Go to Camden, still Class D but more reputable and less of a ripoff. See if you can find a school in places like Bathurst (you can hop a train from Sydney, or hire a car, about a two hour drive) or Dubbo, that way you are already in the middle of where you want to go if you want to see bush. (
)
As the other fellas say, the coastal towns of NSW both north and south of Sydney are beautiful