Here we are on day 11 in New Zealand, and we just sorted out where we are going to live for the next two months! Huzzah and hurray.
Our first week was all set with an Airbnb in the North Shore of Auckland, which turned out to be ideal for us. Much more peaceful than the CBD, very quiet neighborhood (except for crickets and tui!), beautiful views of both downtown and a nature reserve, and walkable to many different shops and restaurants. Our missions were to get settled, take care of basic chores like getting phone SIMs and finding a used car to buy, all while my husband continued to work full-time (remotely of course).
Once TradeMe figured out that we were now in NZ, we got our accounts activated (apparently you can get this done ahead of time by special arrangement) and started scouring listings. They had to be furnished, and they had to accept short-term rentals, and they had to be okay with the fact that we couldn't come to any viewings, since we were only looking at places far from Auckland. This severely limited our choices, as you can imagine, probably mainly on that last point. We also wanted something available very SOON, which was hardest of all.
This would all be easier if we weren't 4 people, I imagine. Hotels and other night-by-night housing isn't so bad as a single person. We could have continued hopping around from Airbnb to Airbnb, or similar sites like Bookabach. It does get expensive though, and we wanted to get settled in so hubby could focus on both work and his job search, and homeschool for the kids.
We were very fortunate that a Facebook friend offered to let us stay with her family "for as long as you like," although we would have felt uncomfortable taking her up on more than a few days! A old-fashioned Kiwi welcome, indeed! Our kids enjoyed having playmates for a change. Even more fortunately, our back-and-forth messages and calls to landlords started to pay off.
I think it helps a lot if you are arriving a bit off-season, because a number of people have holiday homes that they can't keep full outside of summer and maybe shoulder season. We ended up going with an agent in Nelson who advertised some really gorgeous homes on TradeMe, with deep discounts on holiday homes for stays of a month or longer. It doesn't hurt to email holiday home websites and ask if they can hook you up with something like this.
This is still a "top of budget" option, but comparable to what we were paying for rent anyway back home...heh...and once we know what our long term situation is, we can move somewhere cheaper. It's easy while all we have is suitcases.
For what it's worth, the landlords I contacted didn't have a problem accepting references from landlords back home.