I love the second season.
Firstly, a bunch of standout episodes: "Q Who", "Contagion", "Elementary, Dear Data", "A Matter of Honour", "The Measure of a Man", "Peak Performance", "Time Squared" (although I think this one's overrated), "The Emissary", "Loud as a Whisper", "Samaritan Snare" (if only for the Picard backstory).
Secondly, characters! I love Kate Pulaski - a far more interesting character than Crusher. Was she a better fit for the TNG ensemble? No, and I'm glad that McFadden returned as Beverley in the third season. But Pulaski was a much better character - from her gentle, cynical prodding of Data, to her relationship with Worf, to her care and interest in Geordi's vision, and her general humour and strength, I thought she was wonderful. And, of course, Whoopi as Guinan added so much to the second season and the rest of the series.
Thirdly, much better characterisations! Especially Picard - who begun his evolution here from stuffy grump-face to erstwhile, diplomatic, thoughtful, unrelenting leader and father by the third season.
Oh, and Ron Jones was still around!