Half a day does not give you enough time to have a pleasant trip to Cathedral Cove. Even doing the return trip in a full day would not be particularly pleasant, because the drive time would be at least 5 hours return.
You may like to consider a visit to one of the Islands near Auckland, such as Rangitoto or Waiheke.
We suggest you use the "directions" function of Google Maps to see travel times and routes. or visit our Driving Distances page.