Hi there, hope I caught you before you traveled. My wife and I have used our phones in many countries in Europe, we have AT&T and iPhones, and they work just fine there. We have explored several options when traveling, including installing different SIM cards. What we found and used are these options:
Call AT&T and get an international data/calling plan. You can pay by the MB, or get packaged amounts. We got the 20MB plan, it's fine for checking websites of places you might want to visit (tour times, hours, etc...), google maps for occasional directions or checking flight times, etc. This lasts us around a week with pretty stingy usage. You should reset your iPhone's usage counters to keep tabs on usage, it goes quicker than you think. Getting the international SMS/calling plan cuts your roaming rate to somewhat pricey long distance calling, the rate depends on the country you care calling from. A word of caution: some cellular services by nation do not have contracts with AT&T, so the rates there will be exorbitant. You'll have to discuss where you are traveling with the AT&T rep. SMS are $0.50/ea pretty much everywhere we went. We do this every time we travel abroad, and we simply call to cancel the international stuff and move back to our regular rates after we return.
We did not get a new SIM because we'd lose our number and have a new one. Not a prob if you are not worried about receiving calls, only making them; otherwise you'd need to distribute your temporary number to people who might need to contact you. Plus, they'd need to call long distance from your home country to the new number.
Another trick we use: Google Voice. Get it, sign up, get a Google voice phone number. Get Talkatone. Both of these apps are free. Talkatone will allow you to make free calls over wifi with Google voice. You cannot make free wifi calls with standalone GV; GV alone requires both cellular and wifi to be used for calls, that's why you'll need Talkatone. You can also send and receive SMSs with GV for free on wifi, plus it has an online voicemail. The drawback is that it is another number that you'll need to let contacts have (you get to keep it though), and for free calls/SMS you must use wifi - which often must be purchased for a few euros per amount of time in a hotel/hostel. All in all it's still much cheaper than roaming rates. Turn off GV's SMS forwarding feature unless you need it, this forwards GV SMSs to your cell number and would incur the $0.50/ea SMS charge of not disabled. GV also can make international calls without wifi at very reasonable rates, but you'll need to have some money in the GV account and it will consume cellular data time from your package. Switch your phone to "Airplane Mode" and then turn the wifi on to ensure you don't use a cellular network when making a GV call.
There is also the well known Skype, but IMO GV is a better quality.
A little more looking around on the app store will net a few other wifi/data calling apps, but I have only tried Skype, GV and Talkatone.
Whatever you do, make sure data roaming is OFF and all apps that have "push" data switched to manual or disabled. This will prevent them from siphoning data dollars from the apps you do want to use. Turn data roaming on when you need to use it, then turn it right back off.
The main point is that if you use your phone internationally without getting a plan from AT&T it will potentially cost thousands, if you get an AT&T plan it will be only a modest cost depending on how carefully you manage it and if you go the extra length to use wifi only wherever possible you can do it all for the lowest price possible.
That's about it off the top of my head. Have fun!