May I suggest the Justice and Police Museum as well on Wed the 27th? It's just down the road from the Museum of Sydney.

http://www.hht.net.au/museums/justice_and_police_museum

Entrance is $8 for adults.

Personally, I found this more interesting than the Museum of Sydney (maybe I'm just evil). The J&P Museum is based on an old police station and court house, and contains many photos and 'instruments of crime'.

I did both museums in one day earlier this month. After those, it's an easy walk to the other side of Circular Quay to the MCA.

On the 29th, have you considered the Aquarium and the Wildlife Centre? They're on the other side of Darling Harbour from the Maritime Museum. They're a bit of a tourist trap, but I think the Aquarium is quite interesting, and it currently houses the Dugongs, which apparently are 2 of the only 5 in captivity in the world.

Having said that, the Aquarium, the Wildlife Centre and the Sydney Tower have a combo ticket that can represent some savings.

Lastly, when you land into the International Terminal, pick up a couple of the blue booklets that you should see when you walk towards Immigration. These booklets have coupons for various attractions. They're also available from the Tourist Information Centres.