I have to say that one of the coolest songs of the 80s was Split Enz' "I Got You," so weird it was great. It perfrctly conveyed the feeling of being with a babe you know you didn't belong with.
Other great 80s music: almost anything by The Police, "So" by Peter Gabriel, the soundtrack from "The Breakfast Club" is also pretty cool. And the 80s saw the birth of U2 and REM, two of the best new bands of the last two decades, IMO.