I'm too lazy to write a bunch of lists, so here's my two favorite 80's bands with a few songs for each to begin with.

THE CURE (just a few for now)
The Figurehead (download it or I'll kill you)
Cold (download it or I'll kill you)
Lullaby
Lovesong
Fascination Street
Pictures of You
Closedown

METALLICA (useless for me to name for Pat, but it's the goddamn 80's)
Fade to Black
One
Welcome Home
Master of Puppets
Ride the Lightning
The Four Horseman
...And Justice For All
For Whom the Bell Tolls