I have a really hard time picking all-time favorites of basically anything, so here's a list! (lol I'm so sorry, I always do this). If you took away all my hats and only let me keep one, it would be the Braided Wig hands down, but otherwise:
Sailor Hat - I'm a huge sucker for anything nautical themed. I like the pirate hat too but the sailor one is easier to wear with other outfits without looking super out of place
Gracie Hat - it's absolutely obnoxious and therefore one of my favorites
Bun Wig - I don't have it yet but dear lawd do I need it in my life as soon as possible o_o (hit me up if you have one please, I'd love you forever)
I have the hair bow wig but it's not really doing anything for me at the moment. It always looks so good on other people's characters though, I'm jealous. What are you guys doing right? What am I doing wrong? haha. I like the Elegant Hat too, StarlightSong, but I can't find an outfit or QR to go with it so it's just sitting in storage for now
Also! Shoutout to hairpins in general, but most recently the hibiscus hairpin - they aren't real hates but they occupy the hat space on your character so that sort of counts? Ribbons are really easy to coordinate with outfits as well. ...when I die, bury me in ACNL hats...