TNG Season 3, Episode 19 Captain’s Holiday

gain, very little in the way of long-term plot here, but we get to see Picard in a completely new environment – on holiday. Aside from Risa being a not-great idea that the franchise then runs into the ground later, and the camera man on this episode enjoying the skimpy outfits way too much, this is a fun episode where Picard gets to pursue his great passion, space archaeology, and also enjoy a rare bit of holiday romance.

Plot

Strongly pressured by the crew of the Enterprise, Captain Picard reluctantly agrees to take a vacation on Risa, a pleasure planet. Shortly after he arrives, he is kissed by a woman he has never met, in her attempt to fend off a Ferengi named Sovak. Sovak accuses Picard of conspiring with the woman, Vash, who has in her possession a data disc that he wants. Picard has no interest in the quarrel and returns to his room to discover two "Vorgons" who identify themselves as time-traveling police agents from the 27th century, searching for a powerful weapon called the Tox Uthat capable of stopping the fusion reactions of a star. The 27th-century scientist who invented it traveled back in time to hide it. According to their historical records, Picard will locate this object on Risa.
Picard confronts Vash about the Tox Uthat. She claims to be the former assistant of an archaeologist who discovered the location of the Uthat, gave her the disc for safekeeping, and died. Picard and Vash use the information on the disc to determine the Uthat's hiding place. When they arrive at the location where the Uthat is buried, the Vorgons appear to witness the discovery of the Uthat. Sovak then arrives with a phaser rifle and has Picard and Vash excavate the site at gunpoint for hours. However, the Uthat is not there. The Vorgons leave, confused because this doesn't line up with their historical record. Sovak, in his obsession, refuses to believe that the Uthat isn't there, throws away the rifle, and starts digging while Vash and Picard return to the resort.
After their arrival, the Enterprise returns to pick up Picard. He catches Vash attempting to sneak away from the resort and surmises that she arrived days earlier, located the Uthat, and devised a ruse to fool Sovak into thinking the Uthat was lost. She reveals the hidden Uthat and the Vorgons reappear, demanding it. When Vash suggests that the Vorgons may have ulterior motives, Picard has the Enterprise use the transporter to destroy it. The disappointed Vorgons reveal that Picard has acted just as their records said by destroying the Uthat, admit defeat, and leave. Vash and Picard have a final intimate exchange before they say goodbye to each other.