I can provide some info on your questions. I hope it is useful. All depends on how much time you have in your locations.

SYDNEY

Saturdays - Paddington Market (in the central Sydney Suburb of Paddington and bus accessible) Great for craft type stuff but only open on Sats.

Beaches - depending on the months you are there. Try to get up to Palm Beach on the Northern beaches. You can again get a bus there but if you have a car or access it is a great beach hop from Sydney, lots of beaches to stop in on.

Harbour trip. - If budget is a problem catch a ferry boat from the centre to Manly, cheap sights and Sydney harbour is one of the most fabulous anywhere in the world bar none.

Blue Mountains - A very full day trip. If time is a problem try and get a smaller bus tour up there. Not sure of who. The big companies tours are very formulared and not satisfying. Try and get one that stops at Norman Lindsay's house (artist long dead) Great art, statues, grounds etc.

Have a look at http://sydney.citysearch.com.au/Sydney/ - great info.

Aquarium at Darling Harbour - excellent for a look at local marine life.

MELBOURNE

This is miles away from Kangaroo Island which is off shore from Adelaide.

Melbourne Zoo is worth a look.

There are a couple of train trips Puffin' Billy which covers countryside and is quite good, there is another somewhere there too but the city search web site for Melbourne is good too.

Phillip Island Penguins - each day they return from the sea at dusk and waddle up the beach. Quite a sight.

Aussie Rules football match. Interesting and good atmosphere.

CAIRNS

Cairns itself is not too great being a town on a river. North of there is the Daintree Forest, world heritage listed and here you can find cheap and comfortable backpacker accom at cape Tribulation. Great place. From here also you can do a day trip to great Barrier Reef for diving or snorkelling and various rainforest andriver trips.

Port Douglas, a coastal town between Cape trib and Cairns is a nice resort town.

Hope that helps James