One of the things that made Picard such a memorable character is that, once or twice a season, he would break out of the British Sea captain shell and reveal the character beneath, particularly the flaws and weaknesses.
In this regard, some of the best Picard Episodes are, to obviously begin with
- Chain of Command II (There are Four Lights!)
- Family (Picard reveals how much his Bord capture affected him)
- Tapestry (Reveals Picard's stabbing and its effect on his life)
However, I find one of the most striking aspects of Picard's character is revealed while he is offscreen, by Worf, in an otherwise fairly corny 5th season episode called "The Perfect Mate".
PAR LENOR: Perhaps your captain would care to invite us to join him for dinner this evening...
WORF: The captain dines alone.
It's almost a throwaway line, but manages to crystalise a lot about Picard's behaviour and relationships with the rest of the crew. He's never too close to any of them, or anyone, personally, but instead lives and relates to people through his leadership role as Captain, an effectively Father figure to the crew. There's a pay-off made on this during the last Episode (All Good Things - II) where Picard finally joins one of the poker games.
However, I think that the single best Picard moment related to this is his wordless reaction on hearing of Ensign Ro's defection, at the very end of the penultimate episode (Preemptive Strike). Ro betrays Star Fleet for personal, patriotic, emotional reasons, and does so precisely because Picard professionally pushed her into an undercover mission.
Here Picard finally tastes the bitter pill of consequence that he's been dishing out to aliens and miscreants for seven seasons, as his adoptive officer-daughter Ro finally makes her personal, matured, self-determined choice to not live the rest of her life in his perfect Star Fleet family, or by his cherished Federation rules. And after being betrayed by someone he trusted, for reasons he understands but cannot accept, Picard's livid silence makes for a deliciously dramatic conclusion. A crowning moment, no doubt.