Take the SkyBus from just outside the terminal, runs every 10-15 minutes, takes 15 minutes and costs about A$15 one way. Drops you at the edge of the CBD but only a 10-15 minute walk to the centre or you can take a shuttle bus. Taxi is IIRC about A$40 one way

There is a very good river cruise that you can take to see the city from the water - I'll look out details when I am home tonight and send them

There are two main department stores - Myers and David Jones that are both close to the old GPO building. For once the mens shopping was better than the womens and my wife was surprised to see that I had spent more than her! And the prices were very competitive.

In terms of lunch - what kind of cuisine do you like - there's a huge choice and at all price points

If the weather is poor there are some great museums and galleries and the great thing about MEL is that everything is accesible in a fairly compact, walkable area and of course there is also a free tram that circles the city

I'll post some more details later