I tend to think of cinematography as the quality of the photography and lighting more than the composition of a shot, but regardless pretty much anything in the first season stands up well.
When color TV first premiered, it mimicked technicolor films of the day, with rich tones and hues and multicolored, warm lighting that created atmospheric shadows without resorting to the "fluorescent" starkness that 2001 would make de riguer in films. By the mid-1970s, the cinema look would be replaced with a more "natural" look that took away, at least for me, much of the artistic gloss that made TV interesting to watch. Of course films were leaning toward a more documentary quality in the visuals, too, that gave them a kind of grittiness but robbed them of the magic that is so many Hollywood films of the 1950s and 1960s.
For something that is a bit of a blend -- mostly technicolor but with some of the starker lighting on occasion -- check out Robert Wise's "West Side Story." It's a truly beautiful film in many, many ways, but the cinematography is remarkable. It's amazing to me that 20 years later he made ST-TMP, which by comparison seems pretty washed out and monochrome.
I'm not sure a single moment stands out to me, but episodes with very good cinematography include "The Cage," "Conscience of the King," "The Man Trap," "The Corbomite Maneuver," "Mudd's Women," "Dagger of the Mind," "The Enemy Within," "The Omega Glory," and "Court Martial." I do like the way the director tracks the camera in "Shore Leave," and in terms of blocking and the like, it is a very good moment. In terms of action, I also like a lot of what is done during the Cestus III battle in "Arena," which despite its minimalist approach, is as inventive and framed as well as many films of the period, and in various moments in "Balance of Terror," "Where No Man Has Gone Before," "This Side of Paradise," and "The Naked Time." Given the fact that "Balance of Terror" and "The Corbomite Maneuver" are essentially "bottle shows," I think the directors get a lot of mileage out of interesting camera work and effective use of close ups.
