Last time I was in Europe about 4 years ago I call AT&T and asked them if there was a plan for International travel, I was 7 countries and after that they gave a rate of $7/day for unlimited voice/text/data and every time you travelled to another country your provider listed on the phone changed
I thought this was easy and straightforward
Yep, no idea about T-mobile but you can add international roaming on AT&T for $7 a day or about.
When I went to Asia, I went online and set up an international travel plan. It turned out that my phone was useless in Korea (they only had 4G and my phone was 3G) but worked perfectly well in Mongolia. Which is funny, because most of Mongolia does not have a power grid yet it has a nationwide cell phone network.