Ku-Ring-Gai Chase National Park
Sydney is bounded by National Parks to the north and to the south – With Ku-Ring-Gai Chase in the north and the Royal National Park in the south. The Royal National Park is the second oldest national park in the world after Yellowstone in the USA.
These national parks are also great for going to a drive in a classic car away from the stop and go traffic that plagues most of Sydney. There are less roads Ku-Ring-Gai Chase, but still some worth exploring such as West Head, Cottage Point and Akuna bay. The only downside is the current cycling craze means that you might not be waiting for cars, but you will get stuck behind cyclists who insist on cycling in the middle of the road. (I found only 2-3 out of about 20 I saw even moved over a bit to allow passing).
The cost to enter the National Park is $11, the booth down at Akuna bay was manned, but the earlier booth was not. You can probably drive all the roads in about 2 hours, which is a nice drive if you live near the area.