2) Blue Mountains
The Blue Mountains are a world listed heritage and here you will really feel at one with nature. These mountains are named so due to the evaporating eucalyptus oil leaving a blue haze.
There are a lot of tours operating from the city center so you can pick the best tour for you and your budget. Most tours stop off on the way at the Featherdale Wildlife Park for about forty minutes. This is not a huge wildlife park so forty minutes is enough time to see everything.
Once at the Heritage Park you can go on rainforest walks and ride the steepest railway in the world. There is also a great cable car so you can see great views of the mountains.