iTunes Radio says "network unavailable" (on an iPhone 5 w/ 7.0.2)

guessing by when you said "airport network" im guessing thats a wifi network? If so then it should be working, try to go into safari and see if you can access the internet from there, if not its a issue with your wifi network. If you can access it then what you need to do is double tap home and swipe up all your apps, now hold the home and power buttons at the same time untill you get the apple logo, when it turns on see if your conected to your wifi and try to go into music then radio, if it still doesnt work try to disconnect from wifi and try using cellular to access it, if you can then theres an issue with your wifi network like your ISP has the server or ip on a firewall, or your network/router has one, if you cant access it then try to do a restore in itunes and see if it fixes it. Also before you test to see if it works over celluar head into settings and then cellular then scroll down and make sure music is turned on.