It's been said that Australia is four-wheel drive country, and this can be so, but there are a number of other ways of to explore this massive country. Tours and safari-type trips are very well organised, reasonably priced, and depart from Sydney on a daily basis. A vast tract of bush, organised as several national parks, surrounds the city of Sydney, offering incredibly spectacular views across enormous valleys and cliff faces. There are well marked walking trails, but in some areas watercraft and small aircraft provide an exciting alternative. Given the vastness, overnight trips offer the greatest opportunity for extensive exploration.
Most parks have camping facilities or nearby towns, where accommodation is usually inexpensive.
In particular, the Blue Mountains National Park areas have numerous guesthouses and less expensive backpacker-type accommodations. Dive sites are numerous and visibility is normally very good. You can upgrade your current certification or even learn to dive.