Pipi, tuatua, and green lipped mussels
Pipis are smaller and more common; their shells are quite streaky whereas tuatuas are very white. I've only ever seen Tuatua at my mum's beachhouse on the Coromandel.
I recently returned to Auckland after a couple of years away and was delighted to find that the Auckland fish markets now sells pipis. They're cheap - about $5 a kilo - and really fresh.
As to restaurants, it's pretty rare. One of the strange things about NZ - and in particular, Auckland - is that great local produce like this isn't often used. In Auckland, the mussels always used to be really good at the Belgian beer places - Occidental and De Poste in Mt Eden, also there's one in Ponsonby at Three Lamps. Coromandel town has a huge acquaculture industry so some of the restaurants do them quite well.
Can't speak for pipi or tuatua, but I've had great mussels at The Mussel Pot in Havelock (South Island). You can order them steamed in wine and beer, or garlic, white wine and fresh herbs. My favorite was the coriander, chili ginger & coconut milk.
On the Coromandel Penninsula we stopped for lunch at Tuatua Restaurant and Bar in Whitianga. The mussels there were also quite good.
The Mussel Pot
73 Main Rd, Havelock, Marlborough 7100, NZ
Tuatua Restaurant and Bar
45 Albert Street, Whitianga , NZ