There is a good app in the app store (apple)
its called tunein radio this app is free with no advetisement on the app itself, there is also a pro version which cost 69p with even more features
what it does is pretty much has millions of radio stations from your local area to around the world (im currently listening to an all metallica radio in poland), it also does podcasts and even police scanners. its features are (for the free version) save your favourite radio stations and songs, have all types of radio from music to sports to news ect ect, search up your favourite radio stations,has a car mode so you have a very easy touch screen interface when you are driving and much more.
have a look at it see what you think
also somthing you might like is an app called soundhound its an app where if you are listening to the radio or hear a song tap the button it will listen to what your hearing and then tell you what the song is called.