Hi guys,
Salmon Bay is the best place in a SW'er, you can also kite further up at Green Island.
In a Nor' Easter you can kite the downwind side of Natural Jetty at the Southern end of Thompsons.
In a Sou' Easter you can also kite near Natural jetty (southern side), don't kite on the bay side of the jetty because you fall into the 8 knot zone and the rangers enforce it! [}:)]
In a Nor Wester, Narrow neck is excellent fun and you can even work your way out to some small reef breaks. I know it's the opposite end of the island but you can easily jump on the bay seeker bus which drives around all day until about 5pm or 6pm (check as it's a long way to walk home).
Bay Seeker also stops at Salmon Bay. I wouldn't kite Geordie Bay, to sheltered, very busy with lots of moorings (as does Narrow Neck). There are other spots too but many require boat support.
Hope this helps,

Have fun in the clear waters.