Holy Sites — and to a slightly lesser extent, Cultural Wonders — don't seem to interact with adjacent districts.  For this reason I usually place them in the far corners of my territories, where I don't think I'll ever expand to, so the Holy Site doesn't "compete" with my city's quarters.

Am I missing anything, or is this how people generally use them?  They don't give or receive any sort of adjacency bonus that would support their being placed in a city, do they?

Must admit i'm praying I have a "garbage" tile to put them all

They don't have to be connected to the main plaza like the other districts and offer no adjacency bonuses like you said, so find the furthest tile with the smallest base yield and plop them there.

I believe this is how they are to be used in the current configuration.

Holy sites - don't exploit, just provide the stability and faith. So put them on a sterile tile.

(Most) cultural wonders - DO exploit. So put them in a far corner that has high yields that you may not be able to expand to. They will exploit their tile plus all surrounding tiles.

Holy Sites - I usually place them in cities with trade routes passing by to spread my religion more efficiently or to not being converted. 

Wonders - I put them in places with yields as they exploit tiles around, science and gold included ! But beware to not put them in some remote place you can't defend efficiently : I once had the Eiffel Tower ransacked by some violent independent people...

I place my holy sites in the centre of the city and surround them by districts because (I think) it's looks super cool. Sure a common quarters would be more efficient.

Or sometimes I like to create holy districts or holy cities dedicated to holy sites and wonders:

Exactly right: place them on tiles far away / useless tiles. No adjacency needed with other districts.