Australia is huge, it would take far too much time for most people to cycle around the large areas of the country, so you need to pick one location and explore it from there.
Another option plan a longer route covering many locations but this planning takes practice and of course you need to choose a suitable form of transport to get you and your bikes between each location.
Here are some of the highlights of Australia which I believe are great for people wanting to explore on a bike.
This is an option for people that do not have a huge experience with cycling. The roads are generally good and not too demanding.
The Huon Valley is south of the city of Hobart, in the south region of the Tasmania Island.
It is famous for its rugged coastlines and many of the roads provide excellent views out to sea.
You can look at http://www.huontrail.org.au to find more information on the region.
You should set aside around three to four days to cycle around the Huon Valley.
The Huon Valley Map
This is on the mainland of Australia, in the region of Victoria, on the southern tip of the continent.
Like most regions in this country, it is huge, so you have lots of choices.
A great option is to start in Melbourne (which is an incredibly fun city to stay in for at least a couple of days) then head towards Wangaratta. You can either do the whole ride by bike which will probably take you around three days or start the cycling trip from Wangaratta (so you would need to catch a train or get a friend to drive you there).
Wangaratta has some fine mountain views in the distance and is a good place to ride to Bright which is home to Mount Buffalo.
Wangaratta and Bright are only two options, have a look on an Internet map so see what places really stand out for you.
Victoria Area Map
The city of Cairns is another great choice. I personally love hot and humid places like Cairns because I also enjoy watersports like scuba diving but this place also makes a good choice for a cycling holiday.
The city of Cairns is in the Queensland region; basically the north eastern chunk of Australia. The city is right on the coast and while you can ride inland, I think the ride northwest along the coast provides a better experience.
For northwest you could try riding to Port Douglas and Mossman. Port Douglas has the famous Four Mile Beach which is well worth a visit and there are lots of things to do in and around Mossman, like visiting the Daintree Discovery Centre that is in the rainforest and has lots of aerial walkways allowing you to walk through the forest to experience its nature.
You can even ride further up to Cape Tribulation which also has some lovely beaches.
The ride offers lots of spectacular coastline views, take your time and enjoy them.
Take it easy if you are planning your own route, by which I mean set an easy pace.
You can check out http://www.cairns.com.au for information about Cairns and its surrounds areas.