Kumeu River, although a lovely spot, it is way out west. No direct public transport options available (well there seems to be a direct express bus but in the opposite direction which makes sense as people commute to the city for work from the suburbs)
So your options are self drive or uber perhaps.
From downtown AKL you're looking at 30 - 35 min. drive (outside of rush hour).

I would suggest sticking to the vineyards in Waiheke island and rent a car upon arrival. There's also taxis available or you could do an organised tour.
My favourites in Waiheke are Man O' War, Poderi Crisci and Peacock Sky.