I am a U.S citizen. I will be going to China from Australia in November, 2014.

You can try to apply it in Sydeny. When applying, you need to provide your entry permit or visa to Australia.

Since the valid is three monthes, so if time is possible, you are still suggested to apply for a Tourist Type in your own country in advance to make sure you can get it smoothly. It is acceptable if you enter China before the date your Tourist one expires.