Aitutaki's lagoon is close to ideal for kitesurfing. It's large, shallow — averaging one to two metres across much of its expanse — and the southeast trade winds blow consistently from May through October, the same months when the weather is most pleasant. The flat water means you can cover ground fast without fighting swell, and the shallow bottom provides a safety margin that open-ocean kitesurfing doesn't. For intermediate and experienced riders, this is one of the best lagoon setups in the Pacific.
Lessons and equipment hire are available on the island, though the operation is small and the instructor schedule can be informal — confirm availability before you arrive if this is the main reason for your visit. Beginners can learn here; the conditions that make it good for experienced riders also make the learning curve less brutal than a beach with shore break. The best spots shift with wind direction, but local operators know the lagoon and will point you to wherever the conditions are running that day. Go early — the trade winds typically build through the morning and ease off by late afternoon.