Summerisle! Summerisle! Summerisle! Summerisle!
Tom Paxton’s “Going to the Zoo” begins with
Daddy’s taking us to the zoo tomorrow, zoo tomorrow, zoo tomorrow
Daddy’s taking us to the zoo tomorrow, we can stay all day.
And ends with:
Mommy’s taking us to the zoo tomorrow, etc.
Two bands clock in with songs using circular road metaphors and unusual time signatures:
XTC’s “English Roundabout”, which taps out their frustrations with modern life and traffic both lyrically and musically (in 5/4 time), took its inspiration from Swindon’s notorious “Magic Roundabout”.
The Go-Betweens’ dire, sardonic waltz “The Wrong Road [Round]” is also circular both lyrically and musically; it also has one of the longest lyric sheets I’ve ever seen for a song.
Another vote for the “Maypole Song” from the 1973 The Wicker Man. That was the first thing that came to my mind – but then, May Day’s coming around again… 
What about Karl Orff’s Carmina Burana. It begins with O Fortuna, then after some thirty or forty minutes, winds itself back around to O Fortuna
“Honey” by Bobby Goldsboro
Of topical interest to the British, There’s a hole in my budget.
(This is an update of a song several decades old by Flanders and Swann, but I couldn’t find the original on youtube. Text here)
Joe Diffie’s “Third Rock From the Sun” makes a perfect circle.