The essential Picard Episodes of TNG The Measure of a Man (S2E9) Q Who (S2E16) The Best of Both Worlds (S3E26 & S4E1) The Drumhead (S4E21) Darmok (S5E2) The Inner Light (S5E25) Tapestry (S6E15)
A pretty good use of six hours.
There is also Peak Perfomance (S2E21), which has the quote that everyone loves to give:
> It is possible to commit no mistakes and still lose. That is not a weakness; that is life.
The entire episode, though, does a great job of showing leadership and teamwork.
I also like Hollow Pursuits (S3E21).
Despite LaForge and Riker trying to get Barclay transferred off the Enterprise, Picard ultimately directs LaForge to put in the effort to turn him into a better officer. Despite his shortcomings, we get to see Barclay grow into a competent and even key member within the engineering team across the handful of later episodes in which he's cast.
It's important to show sometimes Picard is wrong and the institutions are wrong. And how he reacts to that.
One of my favorites is Star Trek TNG s04e22 "Half a Life". It's excellent scifi that doesn't glorify aging and death and even points out that death is bad despite it being tradition in society. It highlights that death is the worst possible outcome. Worse than nearly all potential difficulties or suffering while living. And it's one of the few episodes where Lwaxana Troi is a genuinely good person. Better even, ethically and morally, than the star fleet standard. Better than Picard. It's just a shame the episode retreats from it's message at the end and does not embrace the true morality Lwaxana explains.
BoBW is honestly more of a riker arc (and the title refers to riker); but Family rounding out the three parter is quite good. Here's a few you missed:
The Ensigns of Command (as a mirror to the b-story data predicament).
The First Duty
Devil's Due
Ensign Ro
Darmok especially for our polarized time. ED Hirsch argued in "How to Educate a Citizen" that the lack of teaching core knowledge in American schools robs its citizens of a shared language to use to communicate. Troi uses "Juliet on her balcony" as an example in the episode, but today I'm not even sure how many people would know even that reference.
And your comment illustrates the point. We've never met but I can relate to you with just the name of an episode because I know the large ideas you're expressing in 3-4 words: I've thought of Picard's speech in the Drumhead often in recent years. Whenever I catch myself having life regrets, Tapestry comes to mind. The Measure of a Man... maybe not relevant for today's AI, but one day when it is, I hope that generation has watched it.