From Maungauika North Head, the North Shore Coast Walk / Te Araroa heads down to the east end of Cheltenham Beach. This is a lovely and sheltered, relatively short beach opposite Rangitoto. It is backed by mostly restored Victorian and Edwardian houses that adds a nice relaxed suburban feel.
As with all these city beaches, the beaches are relatively flat and the tide goes out a long way. Hence, the best time for a swim is when the tide is in but the best time for exploring is when the tide goes out.
Once the tide is far enough out, you can continue to walk around the rocky coast below the cliffs of Takapuna Head, staring at the west end of the beach.