Pine Gap is a little bit of America in the heart of Australia. Literally. Parts of it are American sovereign territory. It's basically a communications center for satellites. I would have thought it would have been used for other orbiting spacecraft, like the shuttle as well, but apparently not. Can't be doing top secret work with civilians hanging around. Also, the civilian budget probably couldn't pay people enough to move to the back of beyond. I suspect it is probably also being used for drone control over Asia. The Wikipedia article says it is used to control geo-synchronous spy satellites, but I don't think any spy worth his salt would put a satellite up that high (23,000 miles). Low Earth Orbit (LEO, 100 miles) would be much more useful. You might actually be able to see something.
Alice Springs and Pine Gap are smack dab in the center of Australia and in the center of this map. Scale is about 1 inch to 20 miles. Place makes Nevada look downright hospitable. Ayers Rock is about 200 miles to the Southwest.