Sorry, I can't help you with a place in Cairns, but we did stay in Port Douglas. I am not sure it would be your idea of fun though because it was a bed and breakfast and it might be a tad boring for you. You can check it out at www.marae.com.au
I just wanted to tell you that if you are looking for something to do, I would highly recommend going on a bush walk and safari in Port Douglas. It was a huge highlight of our trip. Pete does a wonderful job, and I promise you won't be bored doing it! If you want to check it out you can look at www.daintree-specialised-tours.com We also took our reef trip out of Port Douglas and loved it.
For information on Australia in general, I found this site a great source of information: http://www.smallguide.com.au/ It was very accurate and helpful!
Have a great trip. You will love it over there.
Julie