Australia has some free camping campgrounds. Thredbo Diggings is one that comes to mind, near Jindabyne in the Snowy Mountains. The campground provided picnic tables, a tap for water, and a sturdy concrete block outhouse. It seems to me there might have been a nominal fee for going into the National Park, but camping was free.

Also the rest areas along some of the main roads in Australia have a 48 hour stay limit, so a person could conceivably stay there for a couple nights. They are also free and provide limited amenities - outhouses, and sometimes running water. They are usually a little ways out of towns, but if you plan ahead and eat supper in town, they make a decent place to stop for the night.