I always listen to Diamond City Radio when playing FO4. To me, it is a critical part of the atmosphere to the game. The part of the teaser trailer where Nat King Cole starts playing is what actually began to get me excited.
For those who have never played Fallout, the charm and whimsy, along with the brutality of the world is just a part of what makes the world so great. The pre-war world is a very 50's stylized re-imagining of America. It's both very analog, but also technically advanced, centered around atomic energy.
The main radio stations in both FO3 and FO4 continually play songs from the 50's that usually have something to do with nuclear war, radiation, or exploration. So, you could be listening to Nat King Cole singing Orange Colored Sky while simultaneously blasting a group of raiders, blowing them to pieces. There's always just something fun about that juxtaposition.