Major costs are depreciation, fuel, interest on any loan, insurance (liability, collision and perhaps health) , parking, maintenance (scheduled maintenance such as oil changes and unforeseen repairs), and taxes (including tax on purchase and each of the above items).
If you drive a lot in a large city you'll probably accidentally break various rules from time to time (eg. be a few minutes late getting back to the parking meter or making an illegal left turn because of a day/time combination, or missing a complex parking sign limitation), and be subject to fines, towing and impoundment fees, and/or the cost of fighting tickets. In some areas you may have to pay an annual fee to park on the street in front of your own property. If you have to buy a parking space at a condo that may be tens of thousands of dollars and some maintenance fees (though it will usually be a reasonable investment). Even if you have insurance, you may elect to pay small amounts (up to a couple thousand dollars perhaps) to avoid making claims that could make your insurance increase.
Oil changes, wiper fluid, car washes, tires, detailing (sort of a deep cleaning), diesel DEF fluid, and such like can add up, particularly if you go with expensive synthetic oil replaced at the dealer, (say) BMW washer fluid rather than the generic stuff etc. if you do your own washing at home there is an industry devoted to separating you from your money for cleaning products.
As others have said- toll roads and toll bridges and associated fees (video toll fees or transponder fees).
Insurance, especially for new drivers or drivers with a spotty record can be extremely expensive. Some places require regular emissions or roadworthiness tests in order to maintain registration (which in itself has an annual cost, sometimes related to the tyoe of vehicle).
On the more frivolous side, you may be tempted to buy all manner of accessories, from the practical such as car chargers for your phone and GPS to antlers, eyelashes for the headlights, stick figures advertising your family situation, sports flags etc. In some cultures a doohickey of some kind hanging from the rear view mirror or an air freshener is de rigueur.
Some of these may not be directly applicable in Australia, but most should be.
Edit: Here is a link to an RAC (Australia) list of running costs. For example, given the assumptions they've made, a medium SUV (MITSUBISHI OUTLANDER) is said to have the following costs: