Well, T-Mobile free roaming actually works incredibly well in so many countries. It's a bit slow, but it works. And if you pay $5 to Skype, then you can even get very low cost (two cents per minute calls to the US or free to toll free numbers). Or try FaceTime Audio if you are calling another iPhone. However the one case where it doesn't work well is with local calls, so the best thing to do is to find a low cost prepaid provider. Here's the start of list. Turns out it pays to research the different providers where you want: 1. An easy way to get one of their SIMs. The easiest is at the airport. 2. Decide if you just want a "holiday" SIM which usually includes 17 days and a bunch of data. 3. Make sure to bring an extra phone so you can use your US phone for most purposes. 4. If you will ever be back to the country, try to get a prepaid SIM and then you can turn off autorenew. In New Zealand, Canstarblue says that skinny has the best plans, so a little research shows: 1. Their holiday sim package is$30 for 14 days.
2. They also have a $5/week plan with a$2/sim charge.
3. Their SIMs are at The Warehouse, PaperPlus, I don't know if they are at the Auckland airport, I know that Vodafone and Spark are definitely there.

These are both super reasonable.
There is also a separate review just for travelers. The main point is to look in the duty free section before you leave the airport as that saves the 15% GST. Vodafone appears to have this. Their prices tend to be a bit higher though.
The lowest cost options are Skinny (a prepaid brand for Spark) but you normally can't get at the airport. Spark is also a good choice.