Mossman Gorge is a series of waterfalls, and trails with a rope bridge amongst other things. It isn't as spectacular as some of the waterfalls we saw in the Athertons highlands, but still worth a visit. We saw fresh water turtles in the river.
From cairns the other main attraction besides the reef is the rainforest. You could just go to Kuranda on the skyrail where you will see the rainforest. But to be honest I think it is far too touristy, your much better off going further north perhapsstaying in Port Douglas overnight and going to daintree rainforest and cape trib
The Rainforest is another 'Must See' when in Cairns. I was a little disappointed but it was OK. The company I used was Billy Tea Bush Safaris.