Blue Mountains National Park west of Sydney, about 90 minutes by rail. Oh, civilization! I stumbled out of the apartment, walked a half dozen blocks to Central Station, and took a train to the rainforest!
I went to the town of Katoomba, which was well set up to receive tourists and convey them to the park for a modest fee. Felt a bit like Guernville. (With, need I say it again, better weather.)
It was absolutely beautiful. I hiked paths down from cliffs into little pockets of shady wet rainforest, filled with ferns and fungus and running water.