If you don't want to rely on Rarotonga's limited bus service or be confined to a resort area, then you really need your own set of wheels in the Cook Islands. The big rental car companies are based in Rarotonga although you're much more limited in the other islands. Because all the islands are so small, most people prefer to rent a small motorcycle rather than a car. Motorscooters are reasonably cheap and easy to ride.
Road rules are fairly relaxed.
You should keep an eye out for wild chickens, though. Everyone needs to have a local Cook Islands drivers licence. Your home licence or even an international licence is no good in the Cooks. Getting a local licence is is a reasonably simple and laid back process, you can even ride your rental bike to the police station for the test. In Rarotonga you need to get your licence from police headquarters in Avarua.