Just so you know my own personal tastes (before I gleefully head off to bed after this long, long day), here are some of my favourite 80's songs:
Wild Wild West - Escape Club
Baby Got Back - Sir Mix-a-Lot (80's or early 90's?)
Rudy Can't Fail - The Clash
Hold Me Now - Thompson Twins
You Might Think - The Cars
Missing You - John (Jack?) Waite
Paul Revere - The Beastie Boys
Come On Eileen - Dexy's Midnight Runners
Under Pressure - David Bowie & Queen
Shattered Dreams - Johnny Hates Jazz
She-Bop - Cindy Lauper
Mirror in the Bathroom - English Beat
King of Pain - The Police
Poison - Bel Biv Devoe (80's or early 90's?)
Changes - Yes
All Out of Love - Air Supply (shut up)
Glory of Love (from 'The Karate Kid') - Peter Cetera
Down Under - Men at Work
Pictures of You - The Cure
I Want You to Want Me - Cheap Trick (80's or early 90's?)
Anything by Huey Lewis & the News, Billy Joel, Tears for Fears and, of COURSE, 'The Final Countdown' by Europe.
Disclaimer: More of those might actually be from the 90's than I noted--I'm old at the decades are all starting to run together...