Do you have transport? You kind of need a car up there as the public transport is terrible.
If you like the beach then winter is the best time for swimming in the ocean in Nth Qld. Is a fair drive north of town though.
The grandparents took DS1 to the Tropical Zoo while we were last in Cairns and he had a great time, I think that is free for little kids too, but it is out near the beaches.
There is a waterslide park out at Edmonton but I think that is only open on school holidays now.

The lagoon probably isn't too cold if you are not a Cairns local... you get pathetic about the cold if you live up there for very long. And muddies playground at the esplanade is fantastic!
I agree with what the other girls have said about Kuranda. Skyrail and the train ride are amazing.