If you google "best songs of the 80s" you'll find some lists that may be helpful (you won't agree with them all, but at least you'll have a 100 songs or so to skim through - VH1 has a top 100 for example).
A few suggestions for consideration:
Billie Jean
Sweet Child O'Mine
With or Without You
Walk Like an Egyptian
Faith
Little Red Corvette
It Takes Two
What It Takes
All My Exes Live in Texas
Forever and Ever, Amen
Walk This Way (Run DMC version)
Tainted Love (that is one creepy video)
99 Luft Balloons
Livin' on a Prayer