Hey All.
My wife and I kited at Exmouth for 18 months (left there 18 months ago) I believe we were (permanant) kiters # 2 & 3 in town.
Summer is actually the best time to kite on the west side of the cape (very regular SW winds all summer). The beach we spent most time at was Wobiri / Janz (2 accesses onto the same beach). Very nice bay with beach curving right around to the north west so that you will always wash up on the soft sand (after going over just a little bit of reef

) if you run into problems. Nice beginner beach.
Further down the road (to the south) you have a place called Graveyards (unmarked entrance ... you will have to "try" to get a local to show you - or look for kites on the water). Very nice beach if you are into waves ... if you get it wrong however you will end up on very nasty exposed reef. If the track is chopped up you will need a 4wd to get to it (that was when I discovered you couldn't count my Tercell as a 4wd!)
Just North of Tantabidi boat ramp there is another smaller ramp (reasonably nice gravel road to it) this has flat water and a very long beach but isn't into the national park yet (so its free to get to).
Right down the end in the park (You have to pay to get into the national park) you have Sandy bay ... veeeerrrry nice. We had 30 kt winds, no waves, crystal clear water. We were kiting over spectacular coral - if you are lucky you will get dolphins in there too plus the usual turtles.
In summer Exmouth has a standard daytime (summer) temperature of about 45 degC but it is almost always ~10 deg cooler on the west side of the cape (where the wind is). In summer the camping grounds in the national park are empty. At the right time of year all the beaches on the west side will have turtles to dodge (you can aim for them but they are surprisingly quick when they need to be

) and I often saw dolphins (and one mako shark ... nasty).
In Winter the winds are lighter (usually less than 10 kts) and the water colder and the town is packed with tourists. The beaches on the west side however would still be almost empty (except Wobiri / Janz).
Town beach (on the town side ... !) is good for winds from the NE / SE. Most of the beach from town to the top of the cape is good in those conditions ... town beach gets a bit dry at low tide.
dg