Buses, ride share and taxis and are adequate to get around Terrigal. But if you would like to explore outside of Terrigal, such as, Killcare or Woy Woy, they are not easily accessible by bus.
Taxis will get you to places you want to visit, but it will be an pricy option. It is usually cheaper to have your own vehicle and get going whenever you like.
You can get car hire from the Sydney Domestic Airport or Newcastle easily.
Some of the car hire providers available in Syndey and New castle are Avis Cars and Hertz.