I don’t know if “show and tell” was a thing at your school but somehow I had a copy of Another Brick in the Wall vinyl single and played it for the class. I must have been in grade 5 or 6. What a fuckin legend I am haha.
Tallahassee and Beat The Champ by the Mountain Goats.
The Suburbs and Neon Bible by Arcade Fire.
Deltron 3030 by Del the Funkee Homosapien and Dan the Automator.
Edit: how could I forget In The Aeroplane Over The Sea by Neutral Milk Hotel
Not sure if it counts, but In The Aeroplane Over The Sea by Neutral Milk Hotel I think is sometimes considered a bit of a concept album. Not so much with storytelling, but I think it was all connected to dreams Mangum had.
Also, a band I randomly saw at a Calgary music festival, Hard Drugs, their self-titled album was an epic story driven concept album that I highly recommend https://songwhip.com/harddrugs
You know I thought my music tastes was really broad as I like progressive rock, new wave, alternative, etc. Then I sorta realized they were all sort the same off center sometimes touching mainstream stuff over time.
Not sure if Antic Clay's Hilarious Death Blues is a concept album but man it's the darkest double album I've ever listened to, to the point that I would not recommend listening to it while depressed or going through some serious shit. It's a journey through an apocalyptic Americana and its very convincing in its beautiful hopelessness. It's Cormac McCarthy's Blood Meridian made into sonic flesh.
Divers by Joanna Newsom. I love the cyclical arrangement of her songs with the last line of her last song looping back to the first line of her first song. I think it really illustrates what she's trying to say about the nature of love and time.