Hi from tassie.
Sydney is a awkward place to
live aboard, lots of
regulations, expensive and very crowded and
water ways patroling to keep a close eye on vagrant yachts. So make sure you have a spot that allows livaboards before you turn up there.
Many years ago I lived on a
mooring at cammeray marina, middle harbour. Wrong side of sydney for you, but a nice place and friendly people.
Good luck in your search.