The Auckland Steam Engine Society has a page on facebook.
**LINK**
There is to be a steam launch outing on the lower Waikato river at Tuakau on the 12th of March. This is about an hours drive south of Auckland. There is also a guy in Tuakau working on a steam aeroplane, we found him last time we had a steam up there. You might also be able to visit the societies Newcomen engine at a site north of Auckland. This was built for the 300th anniversary of the original.
While MOTAT is still well worth a visit, you should be aware that nothing has been in steam there for several years, since the current management sacked all the steam volunteers. I gather since then a lot of the aviation section volunteers have also gone . The beam engine is still worth visiting, as are the aircraft.
There are club tracks for miniature locomotives in Auckland, Manukau Live Steamers not far from the airport and Auckland Society of Model Engineers at Panmure. There is also a private track on the north shore. I believe Whangarei has a club track too. There is also a steam launch up there.
The Auckland Maritime Museum, on the waterfront in the central city, has a steam launch and is well worth a visit.
I'm not sure if the Vintage engine restorers group would have anything on that month but I might be able to find out. They are into old single banger engines from farms, and tractors and so on.
I'll be out of the country for all of March, but I can help you get into contact with some of the people before I leave on Saturday morning. Send me a PM if you like.
John