I was in Brisbane this past May and just loved it. It's a great walking city and the public transportation rivals the best in the world; commuter trains from the airport and also to the coast, water taxis up the river (in the city), and nice clean buses.
The downtown central shopping district has walking mall that is very nice and lots of other attractions (museums, casino, dining, etc). Also, there is a tourism office on the walking mall with info on hundreds of attractions in/near Brisbane (and within the State of Queensland).
One think I loved about Brisabne was the way the old architecture blended in with the new. It also felt like a "big" small town. With a million people it is not little town but I was able to walk everywhere (my legs did get very tired though). To me it reminded me of Austin, Tx in the early 90s.
Nearby is the Australian Zoo (Steve Irwin's place). I hear it is quite nice but make sure and take the train (it's faster, easier and cheaper then the bus). The zoo will pick you up at the nearest train stop and shuttle you to the zoo.
As for food, if you have never been to Australia before, try the bacon. It's interesting, it is cut a bit different then other places with a larger piece of meet at one end.
Attached are some photos from around town. (my girlfriend loves Tweety, and she could not be with me, so that little guy travels around for some photos with me)