Marie, it's either that nuclear war is currently happening or the scenario is post-apocalyptic. I'm not sure. It's still a strange song. And for clearer context, "vamos a la playa" is a general expression term to make the best of things when something awful or unfortunate happens (my sister at least knew that, back then, even though she totally missed what the song was about!)
http://www.nomorelyrics.net/song/184789.html is the original lyrics. You can translate them in Babelfish:
http://babelfish.altavista.com/
Use Spanish to English.
It's interesting that with two songs on pretty much the same theme (but in another language) that were out around the same time--Nena hit it big, while in the States, at least, Righeira remained in obscurity. Maybe Righeira should've found someone to do a lousy translation for them, too.
Oh, and Schwenko--I did find the other video in youtube. The URL is
http://www.youtube.com/watch?v=q4e1V3HM ... ed&search=
Oh, and one other possibility if we want to try to be literal is that a nuclear power plant accident happened near a beach..