Chelsea: Luna Street.

Above: Luna Street, just south of the King's Road, Chelsea, Schwingin' London. During the early part of 1967, one of these terraced houses was home to Cass Elliot of the Mamas and Papas. Ye will no doubt have guessed where this is heading...
Yep, here it was, probably in late April of the aforementioned year, that Sgt Pepper received its first public airing. Over to Aspinall: "It was six in the morning and we went down the King's Road in cars to see Cass Elliot... We had the album with us, finished at last. She had a great sound system. Her flat was in a block of houses, back to back, really close together, and we put the system on the window ledge and the music blasted through the neighborhood. It sounded great. All the windows around us opened and people leaned out, wondering. A lovely spring morning. People were smiling and giving us the thumbs up."
Macca, when asked to recall in 1994, couldn't really, but did offer this: "It's a dim recollection but I think that's true, yeah. The weekend we finished the album is a bit of a blur. I just remember that we all felt so exhilarated. Pepper had taken 6 months to make - longer than any other album. When we first heard it back, we knew we'd pulled it off."
(As for a precise date, my guess would be either Sunday 30th April, or else the previous weekend 22nd/23rd . Harry Moss cut the final mono version at EMI studios on Friday 28th, and acetates would have been run off for interested parties to be collected over the weekend. Actual work on the album had finished on Friday 21st, so it's possible "rejected running order" acetates were done then, and taken to Chelsea.)
Anyway, whither Luna Street? Those still conscious will note that it doesn't appear on modern maps:

This is because the whole area was demolished a couple of years post-Pepper to make way for the World's End Housing Estate:

All that remains of the titular flat is this photo, showing an interior wall decorated contemporaneously by John under the influence of the dreaded you-know-wot:

And then there is this tree, visible at the southern end of Luna Street in the vintage pics, and still there today, a mute witness to the whole thing, as Prince Charles would no doubt have it:

Palpable nonsense.
A doff o' the cap to the excellent Kensington & Chelsea Library Time Machine blog for local information etc.