Tough choice. Most of my favourite bands have released at least one brilliant live album. Those that come to mind immediately are Strangers in the Night by UFO, Different Stages by Rush, Made in Japan by Deep Purple, Alive in Athens by Iced Earth and On Stage by Rainbow. If I dug a bit deeper, I'd find more that I would kill myself for ommiting. Like How the West was Won by Led Zeppelin.
However, as much as I truly love the above albums, I think three others are very special to me. The first would be Scream for me Brazil by Bruce Dickinson. No particular reason to be found in the album itself, but I have the same emotional attachment to it as I do to almost all of Bruce's albums. The second is Live from Radio City Music Hall by Black Sabbath Heaven and Hell. Even from a tiny Youtube screen, the sheer magic of Dio and Iommi being on the same stage gave me the chills, and I was hoping and praying that I would get the chance to see them live. Which is why maybe Neon Nights could replace this one in my heart - both because it's Dio's last recorded show, and I was there. I haven't watched or listened to it yet, though. Finally, there is P.U.L.S.E. by Pink Floyd. For the most part, the show is pretty good though not really mind-blowing, and there are some moments which I think aren't even all that good... but the one and only reason I will always keep this is David Gilmour's solo on Comfortably Numb, which may well be the greatest moment in rock history. This is what the electric guitar was invented for, and you could almost say that every other solo that came afterwards is irrelevant.