The Royal National Park lies about 30 km south of Sydney, on the Pacific coast. It was founded in 1879 and features an amazing coastline, beaches where bathing is possible, much bushland and some forested valleys. Lots of excellent walking trails, especially those following the coastline! You can find many Australian and also some introduced animals in the park.
A hot tip for quiet nights is the Garie Beach Youth Hostel, which has to be booked in advance, and the door key often to be collected and returned at the YHA head office in Sydney centre.