Atiu Island. Cook Island. Polynesia. South Pacific Ocean. Children dressed in traditional Polynesian dances and interpret Polynesian dances organized at Hotel Villas Atiu Atiu island. The Cook Islands lie northeast of New Zealand in the South Pacific Ocean. Cook Islanders are related to the Maori of New Zealand and the inhabitants of French Polynesia (commonly referred to as Tahiti). Cook Islands dance traditions are kept alive through festivals, celebrations and performances for tourists. Cook