I'm going with the Motels song "Mission of Mercy", which was the b-side of either "Only the Lonely" or "Take the 'L' , their two biggest hits.
As "Mission" was the opening track of that disk, I found it odd that it was relegated to a b-side. I also found it far more interesting song.
Each time I'd end up at Char Bar, which is a bar in Columbus, but back in the day it was located on campus (well across the street) not its current location near downtown. Well, I'd play this song and the Heartbreaker's "Change of Heart".
Fun fact #1: Martha Davis, lead singer of the Motels had the original vocal on "Take My Breath Away" which was made famous when they replaced her with Teri Nunn of Berlin. Berlin has the name on the single, but I don't think they actually played a note, as the "Motels" version sounds note for note the same. It was all Georgio Moroder.
Fun fact #2: the Motels shared rehearsal space with the Go-Go's when they were up and coming bands. The latter band was envious of how much more professional the former was and that they had better equipment.