I needed the cheapest way to pick her up, but knowing she's been through at least 15 hours of travel, I didn't want to force her to take a bus on her way to the city. So here's what I did.
I took the J1 Bus from Currie Street. Any of the J Buses (J for "Jet") pass by the airport. Travel time was about 30 minutes. I arrived about an hour early, but that was okay. My wife's flight arrived about 15 minutes early too.
While waiting, I asked the info booth about shuttle buses that may provide a cheaper alternative to taxis. Turned out there was such a thing called SkyLink and it only costs about A$5.50 per person. SkyLink has 25 designated drop off points, some of them right at hotel doorsteps.
Our hostel was not listed, plus the next SkyLink shuttle would only be available until after an hour, so we just took a cab back to the city. It cost us less than A$15.00.
After that, we had breakfast at Zuma Cafe in Central Market and left my wife to sleep, while I went back to school to resume our group project and to review for our Database final exams.
