I think most of season 2 is underrated (it tends to get lumped in as "season 1 and 2 are lame, season 3 is when it gets better" attitude). However, specific eps, in no particular order:
1. The Royale - how can anyone not love this. When TNG began it seemed to carry over all the serious bits of TOS, without the absurd/funny bits. "The Royale" reminded us there's room for all manner of bizarre in Trek!
2. Family - yeah, people often say they like it, but it's not just 'good', or even 'really good' it is AMAZING!
3. Heart Of Glory - OK, TNG went on to do Klingons bigger and better but I just can't forget when I first saw this ep. Compared to eps like "Home Soil" and "Too Short A Season" that aired before it, it was a breath of fresh air. Genuine feeling of danger, pacing - great.
4. The Schzoid Man - just a solid episode of fun.
5 - The Child - pretty much for those first few minutes. That score! The grand look around the bridge. Riker with a beard!? Worf and Geordi in yellow uniforms!?!
I was going to mention "Lower Decks" and "Measure Of A Man" - but I HOPE that everyone knows how great they are. If not, then consider them bumping Schzoid Man and The Child off the list above!