You would need to turn off 3g and mobile data off and only use wifi in places such as coffee shops etc.
One suggestion if your phone is unlocked is to buy a local sim whilst your there although be careful as some american networks charge you to receive a text message.
If your on contract its free to unlock to all networks or £15 if your on payg.
Travel link : http://www.o2.co.uk/international/o2-travel
Unlock Link: https://www.o2.co.uk/apps/help/help?qid=1&q1=2&route=unlocking&case=Handset%20Unlocking%20Form
Also please be aware when a iphone goes to sleep it tries to switch from wifi to 3g to save battery power.
