The original response incorrectly identified Waiheke Island as a river. Waiheke Island is an island in the Hauraki Gulf, not a river. It lies ~20 km northeast of Auckland, covers 92 km², and has ~8,000 residents. It's known for vineyards, beaches, and tourism.
The closest significant rivers to Auckland city center:
Auckland sits on an isthmus between two harbours: Waitematā (east, Pacific) and Manukau (west, Tasman). The city's "rivers" are mostly short streams draining volcanic terrain into these harbours—no major river flows through central Auckland.
While not a river, Waiheke is a premier destination: 40-minute ferry from downtown Auckland, 30+ vineyards, white-sand beaches, olive groves, and artistic communities. Don't skip it—just don't call it a river.