Tokin hats! Blue ones, purple ones, red ones (especially red ones)! Iconic, elegant, suiting Touhou by being eastern through and through, but at the same time not taking too much space and focus; tokin grabs your attention to the head, but then yields that attention to hair and face without necessary fights, which I find as a good balance (that's why red is best for tokin, being a color that stands out when used only as a smaller touch). I can't tell however if I prefer tokin with pom poms or not, it depends on depiction.
In similar vein, many accessories that are not exactly hats are great in my book. Shoot out to chick's nest on Kutaka's head.
I don't have any hat that I particularly dislike, even Hecatia, while on sillier side, isn't that bad for me. However, between two big groups of hats that I'm neutral to, those two being hats with brim and mobcaps, former wins decisively.