I'm hoping to put together a US to NZ electronics guide sometime soon, based on my experience getting all my gear set up, but the short version is:
1. Buy your transformers before you come to NZ! I bought mine here:
Heavy Duty Step UP and Down Voltage Transformers Thankfully, I initially thought I'd just buy 2, then decided to go for 4. I spent less on all 4 than I would have for just one here.
To figure out which size transformer you need remember this: Volts*Amps=Watts. It's easy to find the information on your gear--look underneath or near the plug.
One huge mistake I made was not checking the vacuum cleaner we brought with us. Rather than ensuring I had a big enough transformer, I just assumed. So I now have a $1000 NZ-bought Dyson and a $2000 US-bought door prop.
2. Check your gear to see if says 'Input 100-240 v 50-60 Hz'. If so, then those items need only an adapter or a new plug. Adapters here cost about $10 each. New plugs for computers, laptops, and monitors are about $12.
3. Adapters, Converters, and Transformers are not the same thing. An adapter just changes the end of the plug. A converter is good for low-power, short use items, like an electric razor, and transformers are the workhorses that can power lots of gear and run for hours on end.
Obviously, there's more to it, which I'll put together soon.