Lynn wants to know she could get to receive internet radio without needing a smartphone. Leo says he uses one from Grace Digital which is also an alarm clock. She would have to have wireless internet access, though. Lynn also wants a portable option. Leo says that a radio over a 3G or 4G connection will do. A smartphone, for instance, can do this with the right app. An iPod Touch would also work. Again, she would still need an internet access, though.
Tablets are also an option. If she's only going to places with Wi-Fi, then a Wi-Fi only device would work. But if she's going all over, she will need a device that has 3G/4G access.
Traveling overseas, all of the EU countries will have common roaming agreements, so she can choose an International Data plan or just buy a local SIM that has data with it.