Hmmm 2-3 days..It appears that your are having the same problem in Australia that I am having for europe.. Lack of Time !!!
I am not a local to either of those places but I have spent a lot of time at each..
will depend on what you are after. If you are planning a trip out to the barrier reef - well there is one day gone... Then I could tell you about fantastic natural waterholes and waterslides out in mountains behind cairns. And then there are things like the Skyway(most expensive option) to the top of the mountains behind Cairns - or you can get up their via the ZigZag railway which winds its way up the mountain side past some magnificant waterfalls. Especially after rain. Once you are up on the Atherton Tablelands there are some great markets, and a massive butterfly house.
Here is my suggestion
for a two - three day stay.
Day one: Barrier Reef take the best tour you can afford out to one of the outer reefs (they are all fun), Day Two: tablelands (zig Zag railway would be my option) Day Three: tour to Cape Tribulation(fantastic place for new years eve - i have done it for the past two years) that covers Port Douglas as well.
As for Darwin: Town is all you are going to get to in one or two days. As everything is so far away - Kakadu National Park is approx 3hr drive. It has to be an overnight trip. Lichfield National park is closer and has some great things to see. This one is a possible day trip with some great waterfalls and swiming holes. And then there are the crocodille tours - just go to the local info booth when you get there - you wont have a problem finding one that suits your budget and taste.
As for getting from Cairns to Darwin - there is no easy way but if you can get
Qantas is much better with the cheapest fair of $287 darwin cairns (2 1/2 hours www.qantas.com.au)
My advice is take it !!
Doing it on the bus is boring as hell and takes forever. I have done it in a car before. And unless you are going to do it as a piss trip taking a week and stopping at every pub you come across... (like that is possible - not a chance in Australia - it would take you 10years)...
if you want any more info - go to my site and send me an email....
Cheers for now - and good luck