The B-side was an instrumental song called "Things to Make and Do".
After DJCarter Alan of WBCN in Boston heard "A Day Without Me" in a record store, he became a U2 fan and included the song in his playlist. Alan's subsequent promotion of the band was instrumental in introducing U2 to a U.S. audience.
The black and white image on the single's slip cover appears to show a footbridge in Booterstown Dart station in South Dublin, and not a Manchester railway bridge as it is claimed. This footbridge looks very similar to the one in the iconic images of Ian Curtis and Joy Division taken by photographer Kevin Cummins in January 1979.
"A Day Without Me" was played live during the first half of the 1980s. On the Boy Tour, it did not have a firmly defined set list position, initially appearing in the main set before moving to the encore. It did not appear on the October Tour until November 1981 (1981-11), when it was paired with "I Threw a Brick Through a Window", a song from the newly released October album. The two songs were linked by a drum segue leading from the end of "I Threw A Brick Through A Window" into "A Day Without Me", and this pairing lasted until April 1985 (1985-04). Since then, neither song has been played live, although "A Day Without Me" has been snippeted on rare occasions. A live performance of the song from Red Rocks Amphitheatre appears on the concert film U2 Live at Red Rocks: Under a Blood Red Sky.
"Things to Make and Do" was the only instrumental ever played live by U2 until the U2 360° Tour ("Return of the Stingray Guitar"), and it regularly followed "The Electric Co." on the Boy Tour. It has only been played once since the end of that tour, at an early date of the October Tour on 31 August 1981 (1981-08-31).