My favorite thing about HxH would be very hard to pin down, but I feel like its characters, structure, themes, etc are all just incredibly memorable and well-done. Overall the series leaves me with a strong longing for adventure, though through a palpably different style from my other favorite battle shounen, One Piece. Ging's chat with Gon at the end of the election arc has to be one of my favorite moments among many.
There are way too many characters to pick a favorite really, but I do love the GonxKillua dynamic which runs through the heart of some of the best arcs (Hunter Exam, Zoldyck Family, Heaven's Arena, Greed Island, Chimera Ant, Election). Honestly, those two probably are my favorite, just for how their dynamics/development go, how it ties into the larger story.
As an ideal I find Ging to be one of the most inspiring characters, but again he's not quite a favorite character. Much as I love his sparring mindgames with Pariston & his scene with Gon, we still haven't really spent enough time to get to know him.