In easily season one's best and most memorable episode, the Enterprise docks at Starbase 74, where they have a number of computer-system problems corrected while most of the crew goes on shore leave. Helping make the repairs are four Bynars, of a peculiar race so interconnected with their computer technology that they talk directly among each other in high-speed digital code. The Bynars represent the series' first truly intriguing, well-conceived, original alien species.
With "11001001," we finally see the series firing on all cylinders, with everything coming together, from plot to character, to sensible use of technology and action. We feel like these are real people in a real universe. The universe may be fictional, stylized, and fantastical, but the story believes in itself and the characters seem real. The Bynars, who have a hidden agenda, distract Riker with a mid-20th-century New Orleans jazz lounge holodeck simulation that features an audience of one — the beautiful and charismatic Minuet (Carolyn McCormick). The scenes in the jazz club all by themselves create such a convincing, atmospheric little universe that they draw us completely into the story's emotional arc — the question of whether a holodeck character can be so real that Riker can fall in love with her. Picard also visits this holodeck simulation, and for perhaps the first time on the series we see both him and Riker as three-dimensional people rather than simply "the captain" and "the first officer." Ironically, this 3D breakthrough is played against a holodeck character.
Meanwhile, the Bynars steal the Enterprise by staging an imminent engineering disaster that requires the immediate evacuation of the ship. It makes for a jeopardy set-piece that's somehow riveting because of its convincing operational detail — not to mention that it's fully integrated into the plot (in stark contrast to, say, the pointlessly drawn-out saucer separation in "Encounter at Farpoint").
In the end, the Bynars' dilemma — at the mercy of a central computer shutdown on their homeworld and needing the Enterprise's computer to preserve their data — becomes the season's most solid sci-fi concept, with the right balance of tech and simplicity. And the character of Minuet — a flawless creation of the Bynars' expert technological grasp — plays a central role in the plot right alongside the questions the character inspires about fantasy and reality. I'm calling it the first great episode of TNG.