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Use Sydney as a base
Depending on your length of stay, you can either travel far and wide from a Sydney base or simply explore the nearer areas within a day's drive or so.
You can do a walking tour of "downtown" Sydney -- we don't really use the term "downtown" -- and be able to discover a number of interesting locations in the heart of the city in only a day or two.
If you wanted to dawdle a bit. there's always the Rocks district, the Royal Botanic Gardens, Darling Harbour, or a quiet time at St Mary's Cathedral...