A cab from the airport to the downtown waterfront area will be less than AU$10 (and what a wonderful exchange rate they have for Americans like me!).
CNS has become *sooooo* touristy. Much of the food is pretty down market. Spend time by the water -- it _is_ beautiful -- but at some point in your life schedule more time in North Queensland and get OUT of CNS.
About an hour away is Port Douglas. Perfect place to stay!
Rent a 4x4 and head up to the Daintree rainforest... then up to Cape Tribulation. There's nothing like it in the world.