My favorite two episodes are Captain's Holiday And Qpid.
Captain's Holiday.
I absolutely adore this episode. It was marvelous to get to see the relaxed, off-duty Jean-Luc Picard suavely romance the beautiful, lady archaeologist. Wonderfully written by Ira Steven Behr, this episode is an homage to the great romantic films of the 40's. Vash is Bacall to Picard's Bogart. Watch Bogart and Bacall in the classic movie "To Have and Have Not" and then watch "Captain's Holiday." Vash's brazenness complements Picard's more sedate personality perfectly. She is the ideal foil for Picard's straight man. Picard and Vash have a very compelling 'battle of wills' dynamic to their relationship. The characterizations and relationship dynamics between Picard and Vash makes this episode a pure joy to watch.
"Is that an order?" Vash
"Absolutely." Picard
"This isn't a starship, Jean-Luc. I don't follow orders." Vash
"From the moment I met you I knew you were going to be trouble." Picard
"You look like a man who could handle trouble." Vash
"Well, any woman who can beat a Ferengi at his own game bears watching." Picard to Vash about Vash
"I'll never forget that look on your face when you thought I was offering you Jamaharon." Vash
"That was a simple misunderstanding." Picard
"You did seem a little disappointed when I turned you down." Vash
"Still think I'm trouble?" Vash to Picard after he kisses her.
"I'm sure of it." Picard to Vash kissing her again.
"Promise me you will try and stay out of trouble" Picard
"I always try." Vash
". . . about that Horga'hn you requested." Picard
"Yes, sir..." Riker (feigning innocence)
"We need to have a little chat about that." Picard
Qpid
If you're going to have someone who is not a Trek fan or even a sci-fi fan watch an episode of TNG this is the episode to have them watch. Like the TOS's 'Trouble with Tribbles,' Qpid is pure, unmitigated fun! The combination of Picard/Vash and Q is unbeatable. Star Trek at it's character driven best!!!
There is also that scorching, absolutely sizzling scene in the teaser between Picard and Vash in his quarters. As Picard watches Vash approach him, the sensual heat in his eyes and in his bedroom baritone practically melt the screen. And then THE KISS!

That boys and girls is some seriously hot romantic chemistry!!!
Just some of the gems from this episode:
"Vash? How did you get in here?" Picard
"I came in through the window." Vash
"Eternity never looked so lovely." Riker
"Excuse me?" Vash
"I was referring to the view. Eternity never looked so lovely." Riker
"You must be Commander Riker." Vash
"I'm afraid you have me at a disadvantage." Riker
"I didn't mean to interrupt. I believe you were about to tell me that my eyes are as mysterious as the stars." Vash
"You're a Betazoid." Riker
"Not at all. It's just that Jean-Luc does very a good imitation of you." Vash
"Nice legs. For a human." Worf about Vash
"I've just been paid a visit by Q." Picard
"Q? Any idea what he's up to?" Riker
"He wants to do something nice for me." Picard
"I'll alert the crew." Riker
"This human emotion, love, it's a dangerous thing, Picard and obviously you're ill-equipped to handle it. She's found a vulnerability in you, a vulnerability I've been looking for for years. If I'd known sooner, I would have appeared as a female. Mark my words, Picard, this is your Achilles heel . . ." Q to Picard about Vash
"You would have me stand idly by as she led you to your destruction?" Q to Picard about Vash
"Yes!" Picard in response.
"Sir, I protest. I am not a merry man." Worf
"The arrow impacted just above my sixth intercostal support, penetrating my secondary subprocessor. Fortunately, none of my biofunctions seem impaired. Do not get discouraged. I believe your aim is improving." Data to Troi after she shoots him with an arrow.
"There's something you should know." Picard
"And what would that be?" Sir Guy
"I'm not from Nottingham." Picard
"Nonsense. You're absolutely wrong. It brought out the best in him." Vash to Q
"His nobility, courage, self-sacrifice. Tenderness." Vash to Picard, intimately.
"You're good. You're really good." Q to Vash
"I'm surprised he wasn't too busy gloating over his victory." Picard
"He was right about one thing, Jean-Luc. As ridiculous as it was, his game did prove you still care." Vash
Picard slides closer to Vash on the couch gazing into her eyes while tenderly stroking her cheek. "I may not share my feelings with my crew, but I do have them."
Warmest Wishes,
Whoa Nellie