Important Notice: Walkway access is presently closed due to sever track damage. It is still possible to access Cathedral Cove by boat. Boat tours and kayak hires can be arranged in Hahei. See here for options.
Cathedral Cove on the Coromandel Peninsula IS the place, at least for many visitors to Aotearoa New Zealand. The main way in is a 40-minute walk from the top of steep Grange Road in Hahei (walk up or bus), or you can walk a track to the start from Hahei Beach for another 20 minutes. There are short side trips to Stingray Bay and Gemstone Beaches.
Cathedral Cove is truly special, surrounded by white cliffs and lined with big Pohutukawa trees. Its natural arch, cave, perfectly clear water, and waterfall put it at the top of many travellers’ to-do lists. In addition, swimming in the beach's crystal clear waters is very safe.
Curiously, you arrive at Mares Leg Cove (according to the official Topo Maps) and must walk through the arch to get to Cathedral Cove.
The only downside? Everyone else thinks it’s also cool to visit and the beaches are quite small. There are parking areas off the Lees Road access and in Hahei. Avoid New Zealand public holidays if you can!