I was more into 70s music at the time, but some of the 80s songs I liked best while still IN the 80s were:
The Police: Synchronicity II (probably my favorite album at the time)
Bruce Springsteen: Glory Days
Genesis: Abacab
Slade: Run Runaway
John Fogerty: Centerfield
Anything by the Oak Ridge Boys. I was 6 when "Elvira" hit big in 1981, and I had such a crush on Richard Sterban at that time! Hard to believe those 4 guys are still together and performing after over 40 years!