There's actually too many excellent things about HGSS to name, for me. I guess I can try, though XD
Gold/Silver are definitely my all-time favourite Pokemon games, and to be able to relive that experience in a totally revamped world was just brilliant. I like that Nintendo waited until AFTER Platinum was released to focus on HGSS, because they were able to include all the great things that Platinum had brought, as well as all the great completely new features (Pokemon following you, Pokeathlon (?), GB Player, etc). That of course and the fact that it managed to retain virtually every bit of nostalgic value.
I suppose one of my favourite things about HGSS was the GB Player. Music is key, to me, and the fact that they acknowledged that people liked the music enough for them to want to hear the 8-bit chiptunes again is just awesome. :)