Dancing competitions are held at the end of April and the beginning of May in the Cook Islands. A visit to Rarotonga with 8 nights stay should fit in these days and you may rent a scooter for 7 days for NZ$ 105 at AVIS. As an alternative means of transportation there is a regular bus, which runs around the island every hour (during night every two hours) and will stop on request at any point. There are single (NZ$ 3), 2 ride (NZ$ 5) and 10 ride tickets available.
For accommodation, I prefer Muri Beach or the adjacent southern coast. You can find a list of accommodations at http://www.ck. Air New Zealand arrives from Los Angeles while it is still daylight so you can easily take the regular public bus to your accommodation and save the cost of an expensive transfer.
I liked the Cross Island Walk but recommend to make it only from the parking in the north up to the Needle Te Rua Manga and the view hill next to it and back. You can save the rest until Wigmore's Waterfall.
During the stay you should visit a dancing competition at the Coco Bar and a dancing show at the Staircase Restaurant (entrance without meal NZ$ 5). You can have excellent meals all around the island (main dishes NZ$ 20 to 25). Only the Italian at Muri Beach disappointed me a lot.
If you can afford the flight to Aitutaki (approx. NZ$ 320 both ways) you should visit this lagoon by all means for 3 to 4 days. For me it was the most beautiful on my journey. A lagoon cruise, including an excellent meal, was NZ$ 65. You should do this twice during your stay by Aitutaki Adventures (yellow boat).
You can have an excellent lunch at Te Vaka Restaurant beside Are Temanu. Twice a week a dancing show takes place at the Blue Nun Cafe (entrance is free but a reservation is necessary for the buffet). You can see that it is a pleasure to the dancers themselves.
In WW II Aitutaki became US air base like Bora Bora. From an old US travel guide I know: "Between 1943 and 1946 three-quarters of the children born on Aititaki were half-Amerikan." James Norman Hall was enthusiastic about the beauty of the girls of Aitutaki, probably also the thousand Amerikan servicemen on the air base. You need to know that neither the government nor the fathers ever payed anything for their children or had contact to them.