At least fair skies or straight out sunshine are my favorites. Clear nights are beautiful too. Basically anything that doesn't limit my view distance to a minimum. It may sound odd, but I prefer to actually see the game :P
One exception is snowfall in Coerthas, especially in Ishgard, where it creates a really relaxing atmosphere.

I mostly dislike any situation, which involves fog, because in my opinion, very few games are capable of implenting realistic looking fog. FFXIV is not one of them in my opinion. Only in Limsa Lominsa, I find fog to be somewhat atmospheric.