Roaming internationally for data can be much more expensive than phone calls.
Data roaming is off by default with the iPhone, and AT&T has some data roaming packages available.
With the iPhone, you can enable Airplane mode followed by turning on wi-fi access. This will disable all iPhone radios except for wi-fi access. You won't be able to place or receive any calls, SMS, or access the internet via the cellular network, but you will have access to the internet via wi-fi.