Definitely visit the Great Barrier Reef.

In north Queensland, I like Port Douglas. Cairns is much bigger, much more touristy-feeling (Japanese language signs on stores, e.g.) Port Douglas is smaller, more upscale, and better positioned to the GBR. Take a medium-size catamaran out to the GBR to snorkel or scuba.

From Port Douglas, it is very easy to reach Daintree. The rainforest is not to be missed.