I've always liked season 2 because the episodes had a slightly darker tone than the rest of the series. There was a sense that space was really dangerous and that there was still an awe and terror at what the crew encountered — the Möbius strip, the Borg, Nagilum and even Q.
Also, I've long preferred Pulaski over Dr. Janice Rand ... um, Beverly Crusher. She also had an arc throughout the season, going from disliking and distrusting Data("The Child" and "Elementary, Dear Data") to being one of his biggest champions ("Peak Performance"). Moreover, she gave both Data and Picard something they were sorely lacking in season one — someone to challenge them.
Fans always seem to get into an uproar about how Pulaski treated Data in the early season two episodes. But that's precisely what the character needed. Characters, much like us real live counterparts, grow and learn when faced with opposition. Up until that point, Data had no opposition and was treated with kid gloves.
The same with Picard. "Encounter at Farpoint" set up Riker as that opposition for Picard, much like Decker was for Kirk in the first third of TMP. Another example is "Yesterday's Enterprise." I thought the dynamic between Riker and Picard in that alternate timeline was how it should've been in the "normal" timeline too.
But any potential conflict quickly fizzled in season one in favor of a father-son relationship that was to deferential.
Pulaski pushed Picard's shit in and challenged his decisions, taking up the role that should've been Riker's. She could also go toe-to-toe with him unlike Crusher. That's because Muldar was a better actress than McFadden, who came across as a shrill, yapping dog when Crusher had to confront anyone (guess Q was right in "True Q").