So I was having a discussion with someone who hates action movies (I don’t think of most of Star Trek as action - just mentioning it) and dislikes sci-fi.
I think of the sci-fi of Star Trek as often being just a vehicle to explore humanity.
What episodes do you think would be best to show someone this side of Star Trek and not overly raise their hackles over Klingon mating rituals and the like?
Measure of a Man:
Measure of A Man
Inner Light
Q Who
Captain’s Holiday
While “The Inner Light” is a wonderful episode, and is not very science-fictiony, I think it also depends on the viewer already being familiar with Picard’s character, and thus might not have as much impact for someone new to the series. It’s been a while since I’ve seen “Family”, so I might be mistaken, but I think that one’s in a similar boat.
I love The Defector - great final scene. Lots of TNG had ‘political intrigue’ and military strategizing that was really narratively satisfying.
I’ve been beaten to the punch by plenty of good choices, and so will just add mention of THE DRUMHEAD.
I was wondering this too about “The Inner Light” - it is my favorite episode, but am not sure how well it will play with someone not used to Picard, but then again - you could probably say that about every episode.
I’m afraid this might be a one shot deal - as if she doesn’t like one I cherry pick for her - I doubt she will be willing to watch any others.
I had to lookup “Family” and didn’t realize that is the only episode Data doesn’t appear.
If you just want to showcase an accessible side of ST, Star Trek IV is the only thing star trek-y that my sister and mom have ever enjoyed.
This. Though I’m not sure how this would be received by anyone not already familiar with Data.
Every great episode of TNG depends to some extent upon the character development provided by every other episode. If we’re going to rule those out, the only episodes left are “Encounter at Farpoint” and “Lower Decks.”
If you’re committed to Next Generation pick an episode where Patrick Stewart is allowed to act and show some degree of emotion - the choices above are good ones. Most episodes of TNG are very flat, the actors show no real emotion, and the stories are more concerned with making social statements than creating any real conflict with people actually acting like people. I have to ask, what are you trying to accomplish with your friend? If you want to show them that they might like Star Trek I think the original series is a much better choice because there’s real chemistry between Spock, Kirk, and McCoy. If you want to prove that Science Fiction is more than just action and tells interesting human stories then I’d suggest something like Firefly or Battlestar Galactica instead. In BSG the first episode, 33, is a great introduction to SciFi for people who don’t like SciFi.
There was a two parter where Picard is being tortured (“there are… FOUR… lights!”), and a Captain [Jellicoe] with a different leadership style is in command of the Enterprise.
Ignoring the sci-fi bits, they touch on some interesting human interaction type of questions.
“Chain of Command” parts I & II.
I would dozenth (which I just discovered is apparently a real word, who knew?) “The Inner Light”. Not knowing the characters may remove a dimension to the story but I think it would still work wonderfully.
“Measure of a man” is also a good suggestion.
For a darker story, “Chain of Command” may work. It is a two parter about Torture (you can probably get away with just watching Part 2 if you include the recap of part 1 since that is meat of the drama).
Don’t feel like looking up the episode name, but the one w/ Wesley and Ashley Judd where everyone’s putting on the glasses and getting hooked on the game that’s brainwashing them… esp. with the recent release of Google glasses 
Hold tight. It’s “The Game.”
IIRC, the Game?
Damnit. ninja’d AND I had no cite.
The Inner Light is a fantastic episode - by far my favorite, and I literally cried one time watching it.
But it’s very much a SF episode. It’s not a space opera episode, but it’s a very “pure” SF story reminiscent of short stories by Clarke, Asimov, etc.
Don’t feel too bad. I still had Memory Alpha open and knew exactly what I was lookin’ for. 
Any episode where all the adults are stupid and super awesome Wesley has to come in and save their bacon again.
OK, real answer. The one where Barkley gets all super smart and takes the Enterprise to that far away place and they talk to the floating alien head.