Uluru

Uluru is probably the most recognisable natural feature in Australia. It is now managed by the local indigenous Australians, the Anangu, for whom it is a sacred site. It is a gigantic lump of 550 million year old sandstone right in the middle of the desert. The nearest town is 470 kilometres away.

I highly recommend visiting Uluru, but because of its isolation I don't think all that many people do -- certainly not in comparison to those who visit Sydney anyway. Fewer than 300 000 foreign tourists visit every year, along with 1.7 million domestic tourists. Sydney by contrast receives 4.1 million international tourists per year.