I need to source a phone for someone traveling to New Zealand and Australia. They need a cell phone to use over there, and don't want to start a new contract. However, they want a US phone number, and they don't want to have to mess with ringback services, or anything funky.
You need a tri-band or quad-band GSM phone (New Zealand and Australia uses the 900/1800MHz bands, and U.S. uses 850/1900MHz bands). So, if you purchase quad-band phone with service from a GSM carrier (basically AT&T or T-Mobile) and get international roaming enabled, you should be able to use that phone anywhere the carriers have roaming agreements with your carrier. This can be pretty costly though.
The easier and cheaper alternative is to probably just buy a pay-as-you-go phone there and use that for local calling. Actually, if you can get your carrier to unlock your (tri/quad-band phone), you can just drop a pay-as-you-go SIM card into it and swap back and forth as desired.