This is a hard album to rank because it really does play as a singular experience -- like an opera or cantata, without any obvious singles to extract.
"A Day in the Life" is devastating... this ghostly, surreal, deathly experience that contrasts so much with the carnival and drug-induced fantasy land of the rest of the album.
If I had to go for it, though...
1. "A Day in the Life" - already addressed it above... simply mesmerizing
2. "Sgt. Pepper's (Reprise)" - I wish this was longer... what a groove they got into
3. "Sgt. Pepper's (Intro)" - rarely does music have a better "world-building" moment
4. "With a Little Help from My Friends" - one of their best compositions and melodies
5. "Fixing a Hole" - criminally underrated, an incredible minimalist guitar solo
6. "Getting Better" - catchy as all hell, and one of the few uptempo songs
7. "She's Leaving Home" - this track is a tear-inducing moment to end Side 1... including a song from the perspective of the parents is a bittersweet touch to round out the album
8. "When I'm Sixty-Four" - an obvious classic, bit of a drop in quality after this one
9. "Lovely Rita" - so trippy, though maybe feels like something from Revolver or Rubber Soul
10. "Lucy in the Sky with Diamonds" - its reputation exceeds its (still wonderful) reality
11. "Being for the Benefit of Mr. Kite!" - cool production, but not much of a song there
12. "Within You Without You" - groovy, but inferior to "The Inner Light" as world music goes
13. "Good Morning Good Morning" - not exactly the greatest melody of all-time
I'd slot "Penny Lane" at #1 and "Strawberry Fields Forever" at #4.5 if you wanted to include those songs from the same session as a part of the rankings.
Only the Beatles could have songs like those, "Hey Jude" and "Revolution," and so many others as singles-only yet still have some of the greatest albums of all-time.
"Penny Lane" - Paul's masterpiece, the best "urban poem" in music history
"Strawberry Fields Forever" - another masterpiece, deliciously weird in so many ways