My 2 cents...
I will NEVER travel without a smart phone again. No, I don't sneak into my work email or try to micro-manage the office while I'm away. But, I do like to keep in contact with family and friends and I find it essential for a relaxed vacation to be able to find directions and make travel/hotel/venue arrangements on-line and on the move. Need to know what bus/tube line gets you to..? Look it up. Can't remember the name of that place you wanted to see? Look it up. Need to make a table reservation? Book it on-line.
That being said, I cannot believe the stupidly-high price of American cell phone providers "international" roaming plans. The only more expensive plans out there are the international traveler (I won't mention brands) you see at the airports and in travel magazine.
My last trip, to London, I spent GBP20 for a pay-as-you-go SIM with 1.5GB of 4G data, free SMS and calling to the US for 3 cents (GBP) a minute (several hundred minutes of calling time included). The SIM also gave me unlimited access to the cellular provider's city-wide WIFI network.
I know I might offend someone's sensibilities because I just made travel more like being at home, but that's what makes me comfortable. I like to take the guesswork out of things so I can explore without worrying about other things. To me, the smart phone became very liberating.
That all being said, all you need is an UNLOCKED smart phone that uses GSM cellular networks. Generally speaking, any newer phone designed to work on AT&T or T-Mobile networks will do, but it MUST be unlocked. These can be found relatively cheap on any of the big internet sales sites or in independent used cell phone shops in your home town. Make sure the phone is a "quad band" GSM phone and you'll be just fine. Once you have your phone, find instructions for replacing the SIM card - easy enough to find on-line if you don't have a printed manual.
I personally run iPhones on the Straighttalk network. While I'm on the plane headed for Europe, I pop out my Straighttalk SIM and when I land, I pop in my 'local' SIM. The process is reversed on the way home so that as soon as I land in the US, I’m back on my home network.
Good luck and have fun.