Hi Wayne, I've been living in Indonesia and Australia. I might be able to share my experience. Sydney for 5 days is actually good enough, You need to go to the Rocks, Darling Harbour, Cockle bay, Circular quay. They're all in the city and can be access by foot. I would also recommend Leichart (little Italy), you can find a delicious ice cream there. It's about 30 mins by bus. The beach that needs to be checked out are Manly, Bondi, Coogee and the Gap. I highly recommend the Gap, it's my favourite spot to see Sydney. North Sydney is also a good place to see Sydney. Food is cheap at Sydney and they have a huge portions compare to US. Oxford st and Darlinghurst are gay area, it's quite interesting. Kingcross is quite famous for Sydney's red district, it's also have a high criminality in Australian standard which means nothing compare to US
The hotdogs and pies in Wooloomooloo is quite famous, you definately want to try that. There's a rib steak joints in Bondi which also quite famous, I forgot its name, it might be called 'the hurricane' For shopping center, QVB, centerpoint and Martin place will keep your girlfriend busy. Homebush is the place for Sydney stadium built for the last olympic. I highly recommend to spend weekend at Sydney. Sydney is the place to party. I used to go to Sublime at cockle bay Sydney has a good public transport system, most of the places I mention can be travel by bus, train or Ferry. I think you will only need to buy a red weekly (probably $26 AUD) to access all the places I mention.
You might want to spend one day to Wollongong, it's a small city near Sydney. It's about 1.5-2 hour drive. They got the biggest Buddhist temple in southern hemisphere. There's also some great beaches down there.
If you can I highly recommend you to go to Melbourne. It's quite a different city than Sydney. It's more european kind of city. 4-5 days should be enough for Melbourne.
I see that you do not put Bali as one of your destination. It's quite ashamed actually what the terorrist have done to Bali's reputation. If you consider going there, I can help you find a trusted guide, my friends lived in denpasar so it won't be difficult for them to find a good guide. Feel free to ask any questions.