As you say, Australia is enormous. It is very hard to say that you have seen the 'real' Australia - we range in climate from tropical to pretty cold on the southern highlands and from desert to rainforest and everything in between. Australia is also one of the most highly urbanised countries on earth. Some say the 'real' Australia is only to be found in country areas but others have a wider definition.
Actually you do not have to go far from Sydney to get into real bush complete with gum trees, koalas and kangaroos - not to mention poisonous snakes and spiders (wear your boots and gaiters - most snakes will keep away from you anyway).
If you want some walking in bush and coast in and around Sydney there is plenty of choice. Here are some suggestions and some links you might like to follow.
Use Google for the following:
* Great North Walk NSW (Sydney - Newcastle)
* Walk Spit bridge to Manly (Sydney)
* Six Foot Track - Blue Mountains
*Walking Blue Mountains NSW
* National Parks NSW - if you follow the prompts you can find details of walks in all National Parks of NSW + map information + tourist information etc.
Suggestions further afield:
* Hunter Valley vineyards - instead of walking you can become legless.
* Google for Kosciuszko National Park - you can say you have climbed to the highest point in the continent of Australia (2229 metres -but you don't have to start from sea-level). The 32 km Main Range Walk is very good as is the walk through Dead Horse Gap.
* If you are interested in caves there are world class limestone caves not far from the Blue Mountains. Website: www.jenolancaves.org.au
We hate to admit it but the Kiwis have some great walking tracks - they call it tramping.
Hope this helps more than confuses.