I think that season 2's first episode "The Child" would benefit a lot from HD as there is a lot more shadow detail in HD
See the lighting info about the episode from memory alpha
[Director Rob]Bowman and director of photography Edward R. Brown experimented with a different, even lower-key than usual style of lighting in this episode. Notably, this is the only episode from the first two seasons where there are no sheets of cardboard on the LCARS displays, which were usually necessitated by the lighting system used. However, Gene Roddenberry and the other producers did not approve of this lighting style, and by the next episode Bowman and Brown reverted to the series' usual style of lighting.
Yes it looked different than the rest of TNG's 7 seasons but it also should show up better in HD than NTSC.
Also people have much better HDTVs than tube televisions from the mid-to-late 1980s capable of displaying higher dynamic ranges.
Actually, a good CRT is going to have better blacks and shadow detail than what's out there today. An HD signal might contain more detail, but in terms of blacks LCDs/Plasmas just can't compare to a good CRT.