Hey Leane,
Depends on how close you want to stay to the airport. The cheapest you'll probably find in close proximity is the Motel Formula 1 which is located at the airport. Otherwise the CBD would be your next best option. I'm sure there would be some fairly resonably priced backpackers with decent facilities & private rooms. I know of a few places close to central railway station which would provide the link to the airport.
A quick search on google would be a good place to start. Let us know how you go.
A320.