Wallis is a terrible place to kite - don't bother.

Tiona park / Green Point / or the sailing club work best in SW, N or NW conditions. There is a large expanse of shin deep water on the eastern fringe of the lake, with the rest of the lake only a couple of meters deeper. The water in the shallows is about 28C at this time of year. There are a few rays and lizards(flathead) around, but they usually get out of your way.
I went out for a couple of hours yesterday, but needed to walk out a fair way to get cleanish NNE air. It's not ideal with anything east in it.
Remember to have $7 in change for the nat park day fee. Otherwise camp/stay at Tiona park.
Self launching can be difficult as there isn't really any beach, but I've found it easier with a fifth line setup(CLS). The picturesque setting sans crowds make this a top spot.