Moreton Is - great spot.
I usually stay with a friend at Cowan Cowan (he is a permenant resident) however can relay the following from my visits.
North Point Camp ground - grassy sites, not much shade, insects (mossies, sandfly's and other various itchy bitey's) can be very very bad, esp. summer.
Mt tempest, Easy walk, hot, some times windy with flying sand can make it a bit unpleasant.
My pick is North east camping zone.
Lack of fresh water is times an issues inwinter but this winter has been very wet. I have drank fresh water straight from the creek/lagoon with no issues but don't tell DERM!
Great afternoon can be spent watching the sun set over the city from the westen beach.
I really hate all the sand though!!! Often cleaning it up months later
Can't think of any more at the moment.