Hey lgringo,
There is really only one place to ride in Cairns itself, and that is Yorkeys Knob. There is no budget accomodation in Yorkeys so you will need to stay at a backpackers in Cairns city itself where there is plenty of budget accomodation. Problem is you then need wheels to get you to Yorkeys which is a 15 minute drive from town.
Your alternative is to go to Port Douglas where if you are lucky you may get a bed at the only real backpackers in PD (Dougies?) It is a 5 minute car drive to 4 mile beach from there.
Sorry dude, but you're in Australia now, you need wheels my friend. Everywhere is long distance in Australia and without wheels of some kind, you are basically screwed especially if you are carrying a couple of kites a board or two and your wet gear.
Townsville is another option, you can stay in the Rose Bay caravan Park and rig across the road if the tide is right, and kite down to the local spot.
Hope you have fun, good winds!