New South Wales has a very organized set of national parks that are complete with cooking, shower, and camping facilites. Among the parks I have visited, The Basin is a stand out. If you live in or around the Sydney area it is the easiest way to get completely OUT of the city in under an hour.
Serviced by several buses such as the L90 from Town Hall/Wynyard Stations, It is at the very tip of The Northern Beaches. When you reach Palm Beach you will need to get to the Ferry Wharf- there is a bus stop. There are ferrys that will whisk you away to camping paradise every hour for around $11.50 Return.
While you wait for the Ferry- across the street is a fish and chips shop- a convieniance shop, and a posh pub/hotel- Barrenjoey House. We sat and had a beer and a wine for a very reasonable (by Sydney standards) $10.50
The ferry ride over is immaculately scenic with the hewn rock islands formed from the sea, Pittwater Bay and the Hawkesbury river all colliding at the tip of the northern beaches peninsula. The Basin Campground is run by The Parks Department and charges a $10 pp fee- you do need to book in advance. http://www.nationalparks.nsw.gov.au/parks.nsf/CampingContent/N0019?OpenDocument&ParkKey=N0019&Type=K
Flat grassy camping area, beaches, gas grills, bush walking, ancient Aboriginal rock carvings, and several trees perfect for lounging in a hammock (note: the one I got in Darwin at the General Store on Cavenagh) bring a book, a Frisbee or just your sense of adventure.