Melbourne is a good idea especially if the only reason you go is to transfer back to the States.
Jason, we've missed your melbournian whit
As suggested if you want to chill - go to Palm Cove.
Don't hang around Cairns itself as pretty boring - Sorry Blair.
Hit the outer barrier reef with an organised trip - at least you'll stay cool in the sea breeze (maybe).
Brisbane will still be hot (not quite as hot as Cairns). Last year was 40+ degrees on x-mas day. Find a pool, a bottle or two or three and become a fish for the afternoon. Whilst in Brisbane visit Stradbroke Island if want to chill or head to the Gold Coast (an hour away) if meter maids take your fancy.
Whilst in Maroochy drive up to Noosa (half an hour away). The wife will love it, plus the beach is pretty good if there is still some sand there.