We've got a local puppet theatre that has performed 'The Hobbit' among other cool stories and is doing 'Rocky Horror' for Halloween! They do a fantastic job and I was thinking of suggesting Lovecraft for next Halloween. What Lovecraft tales do you think would best translate to a fully staged puppet play?

I was thinking 'From Beyond', 'The Cats of Ulthar' or the 'The Music of Erich Zann'?

Music of Erich Zann would be my pick out of those I think, I'm sure there are other good ones but I'd have to go back and browse through them to see which ones would fit the format.

If they do it, would the video be posted online?

Yes, Zoot Theatre Company usually has clips on youtube.

Not actually by Lovecraft, but The Hounds of Tindalos might be another good pick?