My first thought whenever the topic of what episode a person should to introduce Trek to someone comes up is “The Measure of a Man”. Though perhaps a courtroom drama, while certainly something Trek dabbles with on multiple occasions, is not typical enough to fall under the umbrella of conventional.
Maybe something like “Children of the Comet” from season one of SNW. There’s a strange mystery that’s going to spell disaster for a pre-warp civilization, an alien of the week antagonist whom the Enterprise crew needs to figure out how to deal with without getting into a fight, and everything’s neatly wrapped up by the end. The biggest mark against it would be the subplot where Pike’s dealing with the knowledge that he’s going to end up in a beep chair.