ANSWER
The first appearance of a "holodeck" occurred in 1974 on "Star Trek: The Animated Series", episode 19, "The Practical Joker". The word "holodeck" did not appear until later. In this episode it was referred to simply as the "Recreation Room".
True Star Trek geeks know that, although the show was produced by Gene Roddenberry, and featured many of the same writers and actors from the original series, the animated series is not considered "canonical", so it is not really a part of official Star Trek "history". (And yes, I know "Star Trek geek" is not the correct term - don't get me started on that whole "Trekker" vs. "Trekkie" thing.)
WHO GOT IT RIGHT: Bob Milligan, and Marc Quinlivan.
