Hey Josh,
How long are you coming for? I've dived a fair bit up around Tobermory as well as NZ, so can give you both absolute and relative answers!
September is about the coldest month of the year in terms of water temperatures. Coastal diving will be about 12-14 degC (sorry, Fahrenheit is a foreign language to me!) at that time of year. Some of the offshore sites like the Poor Knights will be 1-2 degrees warmer. It's probably warmer than deeper dives in Lake Huron in summer!
Auckland is great in many ways, but in terms of accessible shore diving it's not. There are places like Long Bay that are only 20 minutes or so from the city, but the diving is shallow, fairly murky and not much life around. There is also the (in)famous Lake Pupuke, which is a great training site and very convenient - but it takes a special kind of person to love diving in the lake. At that time of year it's also cold, probably around 8 degC with several thermoclines and even colder as you get deeper.
What Auckland has got, though, is some fantastic diving not too far away. Goat Island is probably the nearest decent shore diving, it's about an hour or so out of town and very convenient as a shore dive. There are a couple of other sites around the Leigh area that are worth exploring as shore dives. You've also got Goat Island Dive who run charters to a number of sites in the Hauraki Gulf.
Slightly further afield you have places like the Poor Knights Islands, the Tutukaka wrecks, the Rainbow Warrior and Matai Bay in the north, that are between 2 and 5 hours drive. I've got photos of the various spots on our website that will give you an idea of what the diving is like:
Photo Gallery - Tech Dive NZ - Technical Diving & Technical Dive Training in New Zealand
Heading south (and east) you have spots like the Coromandel, the Mercury Islands, Lake Taupo and my favourite dive site of all time, Volkner Rocks.
Feel free to get in touch via PM if you want more information, or just post up your questions here!