Driving gives you a measure of flexibility in being able to set your own timetables, go off the beaten track and find some beautiful, often overlooked places. Flying is expensive in Australia, but it does have the advantage of getting you from one centre of population to the next fairly quickly. Don't overlook train travel either, the train network is more comprehensive than the planes. However, you are then reliant on public transport and taxis to get around once you arrive.
From memory and starting from North Queensland, a list of things that may or may not interest you.
Lawn Hill Gorge
Undara Lava Tubes - fascinating
Islands of the Barrier Reef
Daintree township, Daintree River, Cape Tribulation (watch out for salties)
Catamaran and boat cruises to the reef for snorkelling the coral
Hook Island Underwater Observatory
Hinchinbrook Island National Park
Stockmans Hall of Fame - Longreach
Carnarvon Gorge
Fraser Island - largest sand island in the world with perched lakes and wonderful heavily timbered forest, also home to a pack of pure dingos
Glasshouse Mountains and Buderim Ginger
Stanthorpe Glow Worm Caves
Lamington National Park and O'Reillys Guest House
The Gold Coast
Byron Bay Whale watching
Northern NSW beaches for surfing
Coffs Harbour - beautiful beaches, decent surfing, resort atmosphere
Hunter Valley - wineries and magnificent cheeses and other foodstuffs
Sydney
The Blue Mountains and Jenolan Caves
Western Plains Zoo - Dubbo
Merimbula/Eden - deep sea fishing charters, beautiful beaches
The ACT - Canberra - nation's capital, museums, art galleries and don't forget Questacom and Mt Stromlo Observatory
The Coorong
Melbourne
Great Ocean Road
Wilson's Promontory
Penguins at Phillip Island
Tasmania with its rugged, snowy peaks and lakes - the whole island is an adventure and plenty to see and do
Great White Shark cage diving - Port Lincoln
Coober Pedy
Mount Lofty Ranges
Head of the Bight for the Nullabor, Bunda Cliffs and whale watching
Margaret River - wineries, surfing
Perth
Rottnest Island
Pinnacles Desert
Monkey Mia and Shark Bay - semi-tame dolphins and stromatolites
Exmouth and Ningaloo Reef - swimming with the Whale Sharks.
The Hammersly Ranges
Broome and the 3 gorges, Tunnel Creek, Windjana, Geikie - Boab trees - pearl luggers and pearl fishing - return of the migratory wading birds - croc farm - camel rides on the beach
Kununurra and the Ord River and Argyle Diamond Mine and Lake Argyle
The Bungle Bungles
Darwin - so many great things to see and do in Darwin
Bathurst and Melville Island - waterfalls, aboriginal arts and crafts, fishing, island lifestyle
Adelaide River Croc Cruises
Kakadu - waterfalls, saltwater crocs, superb landscape
Arnhem Land - again, magnificent, need permit to get in.
Mataranka Hot Springs
El Questro Station - hot springs, waterfalls, gorges, aboriginal rock art, working cattle station, great place
Devils Marbles
Uluru and Kata Juta, Mt O'Connor and Rainbow Valley
Wolf Creek Meteor Crater
Stanley Chasm, Simpsons Gap and a whole raft of things to see and do in and around Alice Springs.
There ya go and I know a lot of people will have many, many places to add to this.