This is a great question. I like to recommend Data's Day for newbies because he sort of goes around and introduces every character, but it's a pretty unconventional episode.
I think I would go with "Doomsday Machine"!
That said, I also think Darmok would be a good fit too, the concept itself is unique in that as far as I know it's the first it was used in science fiction, but the manner in which the concept is presented "Enterprise crew encounters a problem that can't be solved with guns or technology" is pretty darn representative.