According to John M. Alexander's book The Man in Song: A Discographic Biography of Johnny Cash, the song was written by Charlie Rich and wasn't released as a single:
"Down the Street to 301" was the last track Cash recorded at Sun Studios, courtesy of Charlie Rich. It's a story about a boy who is dating the girl who lives at 301. It appears that they were aiming for a song, and a sound, similar to Cash's giant hit "Ballad of a Teenage Queen." It almost feels like a follow-up to that song, with its doo-wop harmonies and pop production. It was never released as a single, but certainly stands as a fitting finale to Cash's incredible Sun recording career.
— John M. Alexander. The Man in Song: A Discographic Biography of Johnny Cash[4]
^Peter Lewry (2001). I've Been Everywhere: A Johnny Cash Chronicle. Helter Skelter. ISBN978-1-900924-22-1. June Both Columbia and Sun Records release singles this month – "Second Honeymoon"/"Honky Tonk Girl" (Columbia 4-41707) and "Story Of A Broken Heart"/"Down The Street To 301" (Sun 343).