Billy's 1984 concert at London's Wembley Arena, which was broadcast on UK television, can be viewed in its entirety on YouTube, which is a treat for US fans who did not get to see it at the time.
Concerts and Other Live Performances on YouTube Visit the One Final Serenade YouTube Channel for video albums, audio, live concerts, playlists and more, organized by various topics and chronologically.
Video Concerts and Live Appearances These are videos of Billy Joel concerts and other live performances on YouTube:
Concert 2000 Years: The Millennium Concert (New York)(2000) (playlist with video of full concert, pro shot, followed by audio playlist of the album) (thanks to Rob Prisament for posting the rare video)
Concert 2000 Years: The Millennium Concert: Only The Good Die Young (pro shot video on Vimeo)
New Yorker Festival (Oct. 4, 2015) (YouTube playlist) Billy did another Q&A at The New Yorker Festival on October 4, 2015. Journalist Nick Paumgarten hosted and asked questions, as did the audience. This playlist is comprised of fan videos.
Audio Concerts and Live Appearances And there are some concerts on YouTube that are audio only. Here is a list of some of these concerts. I have not posted all of them, there are too many, but focused on the earlier ones. The YouTube channel, The Billy Joel Concert Archive has may audio recordings of Billy's live performances.