I'm live for the last 10 months in Brisbane.
I also wonder why no one kitesurf in the river?
I thought maybe there is a regulation that prohibit that??
Anyway, I run few times a week along the river to both sides, from CBD to New Farm/Tenerife and also to Toowoong.
I think that there are some places with easy approach to the river and relatively low traffic around New Farm park. The place gets winds (is not sheltered), the river is very wide (few hundreds meters), and it's close to the last CityCat station.
On the other side, I saw some jellyfish the other day and heared that there could be sharks too...

Don't know if the shark thing is real.
Any other locals with more information?