Here's a small catamaran that I've used on 3 trips to Cairns (and would book again):
http://www.passions.com.au/
They get a lot of Europeans (I tend to be the only American, or one of a handful). Maybe I'm the exception in that I actually like Cairns, though there is no beach there to speak of (just marsh land with a mile long walkway along it).

My favorite base is actually Mission Beach, about 90 mins south of Cairns with 8 miles of pristine beach. It's right across from Dunk Island, and you can take a water taxi over to it (small resort area). Not a lot of accomodations in Mission Beach, but it's a nice place to kick back for a few days. I would not use it as a base for reef touring, though. If you want to soak up some sunshine, and do some hiking on the island, I would recommend it. The one major hotel is the Mission Beach Resort:
http://www.missionbeachresort.com/

I know there is white water rafting further south near Tully, but haven't done that myself.