As an American planning to go home after the HSC, I feel I may be a little more enlightened on the situation.
The Ivy League schools are immensely hard to get into. As in IMMENSELY. You have to have more than just a good UAI or SAT score, such as your entire high school record, character recommendations, a college essay (that is becoming more and more important to distinguish students), interviews, etc. Also you're competing with more than 30,000 other kids that have been working for years to get into these universities.
Ivy League schools don't give scholarships or the like. Financial aid is also severly limited, basically because they don't have to give it to you. There are thousands of other kids out there with the money to pay, so why bother giving it to you? (that's the theory behind it).
Also, there are a lot of extremely good schools that aren't Ivy League, like Stanford and also a number of East Coast schools.
If you're really interested in going to the States for college, then the deadline for the SATs and thus application is pretty much passed. There is an SAT test at Macquarie on the 4th of December but I'd imagine it'd be pretty booked.