Someone upthread mentioned Warren Zevon’s “Stand in the Fire,” and it’s definitely in my top 10. Zevon was newly sober and sounds ferociously liberated, tearing his old material to shreds, making up lyrics about James Taylor and Jackson Browne, and just having a blast. Fun fact: most of his band on that tour was originally a Zevon tribute band (if you can believe there was such a thing c, 1980).
His solo live “Learning to Flinch” from the 90s is also well worth a listen.
That made me laugh, so people can have extremely divergent opinions. Well then…
I forgot Lou Reed’s Rock and Roll Animal! How could I?
And the Independent thinks it has the definitive answer to the OPs question. I don’t agree much, but hey, they get paid for what I do for free, so they must be good at it.
Yeah, but I bet you know that Ya Yas wasn’t “the first Stones first official live release.”
You know what I love best about “Got It Live If You Want It”?
Photo of the Stones on the back side of the album cover with Charlie Watts wearing Weejuns! 
I forgot* It’s Great To Be Alive* from the Drive-By Truckers.
I managed to end up in the artwork for the album!
Genesis - Seconds out
Average White Band - Live at the test - the whole CD is hard to find these days, the standout is pick up the pieces but the version on this CD is really a jam session - well worth finding.
https://www.youtube.com/watch?v=BciFJFrssSQYou’re all wrong… Mott the Hoople Live
How can anyone be considered “wrong” concerning their favorite live album? After all, that’s what the OP was asking for.
Anyways…my favorite is Steve Harley & Cockney Rebel’s “Face to Face”.
Of course Dylan Albert Hall.
The Band et al, Last Waltz
Bob Seger, Live Bullet
Can’t…just engaging in a little hyperbole. Seriously though, can’t believe Mott the Hoople Live hadn’t been mentioned.
Echoing Dire Straits “Alchemy”. It just never gets old. And watching Mark Knopfler’s amazing guitar work on the dvd makes me grin like a fool.
Add Pink Floyd’s “Delicate Sound of Thunder” and I’m a happy camper.