I live in Sydney and so should be able to point you in the right direction. Generally speaking, we don't get much wind in the mornings. After lunch the sea breezes kick in and that is the best time to get the kite out. Generally, any wind from the east tends to be cross/off shore on most Sydney beaches.
During december the winds can be a little gusty. You can probably expect winds of around 10 - 20 knots during December. You can check the wind conditions in real time by vistiting http://www.ozwind.com.au/newstuff/nsw02.php3
There are plenty of good kiting beaches in and around Sydney. The problem with the beaches around Sydney is that they get very crowed during the weekend, not so much with kiters but with people sitting on the beach roasting themselves. Except for a few surfers, there probably won't be too many people on the beaches during the week, and so this would be the best time to get the kite out on the beaches around Sydney.
Personally, I tend to avoid the beaches around Sydney at all times. Instead, I usually drive about 1 to 2 hours north of Sydney where you'll find some absolutely great (very uncrowed) beaches for kiting. The same can be said for the beaches south of Sydney.
Are you coming to Sydney from overseas ? If you like, drop me an e-mail at firstname.lastname@example.org
and I can give you some specific details on beaches to check out. When are you planning on being in Sydney ? I will be away for a week during December, but if you'd like to meet at some point I'd be more than happy to show you some of the local kite beaches.