If the item you plan on plugging in is a low-wattage unit such as a cell phone, MP-3 player, or electric shaver, most Australian hotels have this neat little plug in the bathrooms that accepts both Australian and North American plugs. It also steps down the voltage to 110v when using the North American plugs. If you plan on plugging anything more than a few watts (in particular travel irons and especially hair dryers) you won't be able to use the bathroom plug.
As already stated, if it's a universal voltage appliance (many are, especially cell phones, shavers, and laptops) you just need an adapter plug obtainable at any travel store, electronics shop, or the luggage sections of WalMart or Target. Otherwise you will need a voltage converter rated for AT LEAST the wattage of the highest-wattage appliance you plan on plugging into it. These voltage converters usually include plug adapters as part of the package, or you can buy the adapters separately if you don't need to step down the voltage.
If your laptop uses a grounding plug (such as Dell) these adapters are a bit hard to find. You may need to go to a specialized electronics shop for one of these. If you plan on surfing the internet with your laptop via a dial-up connection, you'll also need an adapter to allow you to plug into Australia's phone system. Be careful though, if your hotel is using a digital-type phone system this will destroy your laptop's modem. If the hotel has broadband (wired or wireless) this won't be an issue.
Also, if you need to wake up to an alarm and don't want to use your watch or cell phone alarms, buy an inexpensive battery powered alarm clock. Don't bring your clock radio from home as it won't work even with the proper adapters and voltage converters, due to Australia (like almost all 220 volt countries) operating on 50 Hz AC cycles, vs. North America's 60 Hz cycles. Plug-in clocks rely on these AC cycles to keep time accurately.