Akin to the original series effort "Shore Leave" in its claim to being a classic, "Captain's Holiday" is an excellent deviation from your standard Captain Picard episode.
On the basis of the debut for Vash, this one would be a milestone. Vash is basically the Next Generation equivalent of Harry Mudd, a character who made several appearances despite not necessarily adding to the overall legacy of the original series. She returns in "Qpid" and the Deep Space Nine episode "Q-Less," which interestingly leaves the same distinction for the character with Q.
Here and in "Qpid" she's an unlikely romantic foil for Picard, a classic example of opposites attracting. Perhaps a younger Picard would have had much more interest in pursuing her, but the older model only finds her interesting on a sexual level (when he warms to the idea, because at first it's a vacation destination impishly suggested by Riker but not otherwise explained), and the fact that they share archaeology as a passion. Their artifact hunting here just so happens to also feature the classic Star Trek staple of timeline shenanigans, a weapon from the future hidden in the past.
And yes, Vash technically counts as a pop cultural predecessor to Lara Croft, Tomb Raider.
Anyway, the episode is a lot of fun. It introduces Risa, the quintessential Star Trek pleasure planet, handily replacing the one featured in "Shore Leave." Risa is a major feature of two later episodes, "Let He Who Is Without Sin..." from DS9 and "Two Days and Two Nights" from Enterprise. In terms of an impact on the franchise, that has got to count for something.
Aside from all that, it is a sign that looking for different ways to present Picard can frequently lead to some of the show's best material, another reason why the third season is so crucial to the series, because it's the point where the best initial efforts in this regard are made. The same thing happened in DS9's third season with Sisko, by the way, arguably Enterprise with Archer as well.
franchise * series * essential * character
Memory Alpha summary