What's good in season 3 depends on what you're looking for. In the unremastered versions, the special effects (shots of the Enterprise, especially closeups) are generally the best of the series, with better detail and several new and imaginative setups. And all of the music original to season 3 was good or excellent. The scripts, on the other hand - well, the best that can be said about some of them is that they elicited superior effects work and music scores.
Under the circumstances, it seems easier to advise someone new to season 3 concerning what to avoid, rather than what to seek out; there is no third-season episode that's not ridiculous in one aspect or another, as much as I enjoy some of them. I would say to avoid outright three of the 24 episodes - "The Mark of Gideon," "The Lights of Zetar," and "And the Children Shall Lead." A few other stinkers are partially redeemed by a good guest star (Michael Dunn in "Plato's Stepchildren," Jeff Corey in "The Cloud Minders"); a number of others are built around a decent albeit poorly executed idea ("For the World Is Hollow...," "Wink of an Eye").
My favorites are two that are among the weirdest in terms of story content ("Is There in Truth No Beauty?" and "The Empath," produced in sequence and both with original George Duning scores) and one that is probably my pick for best all-around episode of the season despite its improbable aspects, "Requiem for Methuselah." One thing all three have in common is an extended scene with original music but no dialogue: the saving of McCoy in "The Empath," the psychedelic mind-link between Miranda and Spock in "Is There...," and the dance of Rayna and Kirk while Spock plays a complete waltz in the style of Brahms (written for the show by Ivan Ditmars) in "Requiem."
NOTE: "Don't let prejudice and rumor sway you" (as Colonel Greene would say in a later episode) concerning the space-hippies episode "The Way to Eden." As I've written in reply to an earlier post, that episode was likely an attempt to cash in on the mega-popularity of the then-new Broadway musical "Hair" and should be understood as such - and the songs sung by Charles Napier et al. weren't bad.
NOTE 2: I saw most of these first-run at age 12, Fridays at 10 pm Eastern on NBC, and the opinions of later generations of viewers may differ accordingly.