Hey Stig,
There are quite a few spots down Batemans way, notably broulee and moyura. Moyura can be flat on a ne to the south of the breakwater, but depends how much swell there is. Conjola can also have some flat water up at the north end. There are some lagoons that a kiteable, but I usually hit the surf or downwinder, so hopefully someone can point those out. .
For option a bit further away check:
http://www.nswkba.com.au/locationsAnd
southcoastkitesurfing.com.au/index.php?option=com_content&view=article&id=25&Itemid=167I am also in Canberra, and will be heading down to kite/sup/surf on quite a few weekends through the summer.