As do many tiny countries, the Cook Islands derive a substantial chunk of their national income from the sale of stamps and coins. So the Philatelic/Numismatic Center in town (Avarua) is the place to stop if you’re a stamp or coin collector. I’m only a casual philatelist now, but beautiful Aitutaki stamps still make my mouth water. When I was a kid growing up in a public housing project, my only ways of exploring the world were watching nature shows on PBS and asking people to give me stamps from exotic places (like Canada), so stamps still hold a special place in my heart. I bought several sheets. I also bought a Cooks 3 dollar bill. You’d think that you could just bring one home from the change you get after buying a magnum ice cream bar, but the local currency disappears into tourist pockets faster than it can be printed and coined. All of the local money is New Zealand currency.
The Cultural Village is a place I’d recommend. The Cooks don’t get millions of visitors, so the people in their teens and twenties dancing and showing crafts and cultural practices are all quite genuine. They don’t have the zombie glaze of Las Vegas presenters who’ve spoken the same 12 lines 80 billion times. And the meal, featuring things like rukau (taro leaves cooked in seawater) is delicious. Afterwards you can take the circle island tour which helps you identify the spots you’ve gone by 5 times in the local bus and didn’t understand.
In some places you can sign up for an umukai - like a luau (the earth oven used all over the Pacific is called an umu here – imu in Hawaii). On Fridays there are island nights (Polynesian dancing – which Cook Islanders are known for). And on Sundays there’s church. (Don't wear shorts or bikinis or cut offs or tank tops unless you want to be pummeled with a taro root and then struck by lightening.) The entire country closes up shop on Sunday (the missionaries are gone but their influence remains), and the local churches support themselves with tourist visitor donations on Sunday, so it’s a way to help the local community. And you might be invited for muffins and chat afterwards.