Well, I have been celebrating the recent release of all Beatles albums on Amazon Prime by listening to all the albums of my youth… so I’ve also been hearing a lot of intriguing first lines:
“Oh, flew in from Miami Beach B.O.A.C.”
“Desmond has a barrow in the market place”
“Now somewhere in the black mountain hills of Dakota”
“You say you want a revolution”
“Joan was quizzical, studied pataphysical”
“I’d like to be under the sea”
“She came in through the bathroom window”.
etc.
Garland - that was exactly my original intent - not just “this song tells a really cool story.” That’s why I gave the examples I did. Compelling, never-heard-this-before, stop-you-dead-in-your-tracks opening lines that establish time, place, mood, and character. Not every song posted above necessarily meets the criteria I had in mind, but still - everyone’s having fun, so that’s all good!
On a dark desert highway, cool wind in my hair
Warm smell of colitas, rising up through the air
Up ahead in the distance, I saw a shimmering light
My head grew heavy and my sight grew dim
I had to stop for the night
There she stood in the doorway…
Lots of Kris Kristofferson songs will work for me; somebody already mentioned “Me and Bobby McGee,” and then there’s “Sunday Morning Coming Down”
Well I woke up Sunday mornin’, with no way to hold my head that didn’t hurt
And the beer I had for breakfast wasn’t bad, so I had one more for dessert
@GMTplus7 --sadly, when I see those lyrics, I eventually remember “You can check out any time you like, but you can never leave” which evokes Roach Motels in my mind. 
Fatal fascination for the seedy part of town
Walk down the street and your head spins round
Don’t be seen alone without your friends at night
Take a gun or a knife to the low life
Mood and tone - but no character. Still telling a story instead of revealing a character.
He was taken in the night,
They came without any warning.
No time to hide or fight
They came like the bees a swarming.
-Johnny Clegg “Warsaw 1943”
This may be a little closer to what you meant. Also, a lesser know artist that I encourage everyone to check out.
Daddy drank the Sterno (cold beans again tonight)
California Dreamin’
All the leaves are brown (all the leaves are brown)
And the sky is grey (and the sky is grey)
I’ve been for a walk (I’ve been for a walk)
On a winter’s day (on a winter’s day)
I’d be safe and warm (I’d be safe and warm)
If I was in L.A. (if I was in L.A.)
Mamas and the Papas
Interesting one, travelnut - the character isn’t really fleshed out til the lyric of “stopped into a church, I passed along the way, well, I got down on my knees and I began to pray,” but I’ll grant that one A personal favorite song of mine!
It’s true that it is a slow intro where scene precedes character, but a hint of character comes in following verses. Perhaps it leaves too much to the listener’s imagination for this focus.
Little ditty about Jack and Diane
Two American kids growin’ up in the heartland
Jackie gonna be a football star
Diane debutante backseat of Jackie’s car
I’m on the fence as to whether this one fits my criteria, since it’s the actual dialogue of the character versus an observation, and you’ve got to get to the chorus before you realize the guy is a frustrated salesman, but I think it might be in the ballpark.
Look at them yo-yos, that’s the way you do it
You play the guitar on the MTV
That ain’t workin’ - that’s the way you do it
Money for nothing and your chicks for free
There’s a lady who’s sure
All that glitters is gold
And she’s buying a stairway to heaven
Hey Eddie, can you lend me a few bucks
Tonight can you get us a ride
Gotta make it through the tunnel
Got a meeting with a man on the other side
(Springsteen, “Meeting Across the River”)
Roland was a warrior from the land of the midnight sun
With a Thompson gun for hire,
Fighting to be done.
The deal was made in Denmark
On a dark and stormy day
So he set out for Biafra
To join the bloody fray.
Warren Zevon - Warren the Headless Thompson Gunner
I saw a werewolf
with a Chinese menu in his hand
Walkin’ through the streets of Soho
in the rain.
He was lookin’ for a place
Called Lee Ho Fooks
Gonna get a big dish of beef chow mein.
Warren Zevon - Werewolves of London
This song makes me cry, as my MIL has Alzheimer’s:
Is it all in that pretty little head of yours?
What goes on in that place in the dark?
Well I used to know a girl and I could have sworn
That her name was Veronica
(Elvis Costello, Veronica)
If Garland is still reading, she will appreciate this:
When you get out of the hospital
Let me back into your life
I can’t stand what you do
I’m in love with your eyes
(Modern Lovers, Hospital)
Well he went down to dinner
In his Sunday best
Excitable boy, they all said
And he rubbed the pot roast
All over his chest
Excitable boy, they all said.
Warren Zevon - Excitable Boy