Hey Tom, just got back from Shark Bay and although the wind wasn't the best we still got out a few sessions in. From what we have found, your preferred wind direction is westerly-southerly-east and you can kite straight out the front of town...just launch from the southern end of town. There is enough beach there and a couple of wooden shelters to tether your kite to. The water out the front here can be choppy, but the more the tide goes out the more the chop decreases. The water can get fairly shallow, but on a TT you shouldn't have a problem.
Alternative places, are just north of town. Head through town to the end caravan park and go up and around the hill...back down it and you will see a turning on the left. This will take you around to the sand bar you can see. You can rig your kite up on that sandbar and launch from there. Just watch the beach as it can have a few sharp shells lying around and may cut if you are self launching. The third spot you can try is up at Little Lagoon, it is pretty cool spot to go to but it is gusty as and quite frankly a pain in the @rse. Worth doing for ships and giggles.
All these spots are flat water, and we haven't kited any where else. Nanga may also be ok. Don't think I would bother with Big Lagoon, worth the drive but would probably suffer with the same issues as Little Lagoon.
Enjoy.