We currently live in Florida. New Zealand has always fascinated me so any information would be helpful.
The biggest cost I find in NZ vs N. America is the price of food. The difference is so great that it's not even comparable. My wife flew over to Canada (BC) for 3 weeks and could not believe 1kg (2.2lbs) of blueberries for $4 CAD while in season in NZ, that would be $20 NZD. There is a huge reliance of buying produce when in season while in the US/Can, NAFTA covers most of the problems of price fluctuations throughout the seasons (ie. lettuce from California, Mexican limes, year round). So for a comparison, minimum wage in NZ is considerably higher than in the US, the level of difference can't simply compare to the buying power say a $1 USD gets in the US, despite minimum wage in NZ nearly $15/hour (if USD minimum wage is 1/2 of NZ, it certainly only buys a fraction of the US minimum wage equivalent). A quote from my wife says "People in N. America are SPOILED by choice".
Costs like cellphones, TVs, appliances, don't really take a large bite out of the day to day living in NZ. They may be comparable in the US but really, $100/month for landline/broadband isn't a lot out of the bi-weekly pay cheque. The big costs such as mortgages (NZ residential rates around 4.25% p.a. - which is considerably higher than in N. American bank interest rates) are typically the biggest costs.
Then there's the factor that "what you pay here in NZ isn't what you would get in USA". The quality of items for what you pay rarely matches. This even accounts for food - ie. citrus fruit - where NZ doesn't have a highly favourable climate to grow oranges etc.