John Lennon wrote "Bad to Me" while on holiday in Spain in April 1963. The Beatles never released a recording of "Bad to Me", although Lennon recorded a demo.
The song was then given to Billy J. Kramer and the Dakotas (released 26 July 1963), for whom it became a number 1 hit.
Formal structure of "Good Day Sunshine":
Intro 0:00-0:08 uncertain (E?)
Chorus 0:08-0:20 B major
Verse 1 0:20-0:37 A major
Chorus 0:37-0:49 B major
Verse 2 0:49-0:57 * A major
Solo 0:57-1:06* D major
Chorus 1:06-1:18 B major
Verse 3 1:18-1:34 A major
Chorus 1:34-1:46 B major
Chorus 1:46-1:58 B major
Coda (chorus) 1:58-2:08 ambiguous (F major? C major?)*
Comments: Tonally, this is the most sophisticated of Beatles tunes so far: 3 explicitly clear tonalities (B major, A major, D major) and two sections with ambiguous tonal orientation (the intro and coda).
The coda is an extension of the chorus, taking the last two measures of the chorus and jacking them up a half step. This is the same modulation (up a minor second) that was used in  "And I Love Her".
The solo replaces the vocals for the second half of verse 2 (also found in  From Me To You,  "A Hard Day's Night",  "The Night Before",  "You Like Me Too Much",  "In My Life",  "Taxman",  "I'm Only Sleeping", and  "For No One").
Lastly, "Good Day Sunshine" is just the third Beatles song to date to use contiguous choruses (the three precedents being [44b] "Kansas City/Hey Hey Hey Hey",  "I'm Down", and  "Think For Yourself").
Last Thursday I played cocktail piano music for the Grace Academy Graduation Fundraiser at the Bushnell. Naturally, I played some Beatles rep, and discovered an interesting similarity in the chord progressions of Lennon's "Girl" and Harrison's "Something". Though not identical, there is clearly a strong correlation between the two progressions. This similarity is illustrated by the graphic below (click to enlarge).
This blog is a workshop for developing my analyses of The Beatles' music.