Anything featuring the Andorians. So their first episode, "The Andorian Incident" and surprise return in "Shadows of P'Jem". "Cease Fire" is a solid stepping stone toward the Federation, while showing the Andorians like the Vulcans, aren't exactly going to cooperate with each other easily.
"Breaking the Ice", "Fallen Hero" and "The Seventh" are Vulcan espionage stories. I found something interesting about them, while others were turned off by how, dare I say, often illogical and sneering they were. Prejudice toward aliens, and even sections within their community. There's an exploration of the 22nd Century political situation in virtually anything where the Vulcans figure.
I quite like "Fortunate Son" covering that Earth Cargo ship, and the perspective of civilian workers out in space, with Starfleet beginning to encroach on their way of life.
Anything featuring major tech developments like "Silent Enemy" where they realise the NX-01 isn't fully equipped to meet the threats they keep coming up against and rush to install more phase cannons. There's Hoshi Sato developing the Universal Translator and Malcolm tinkering with force fields in "Vox Solis", when the ship is invaded by a tendril creature. "First Flight" is Archer reminiscing about the Warp 5 program. Pretty much any show where the prequel setting is important and taken advantage of. Places where previous Trek couldn't do that idea, or Enterprise goes about it differently enough from say a Next Gen or Voyager story.
