I've compiled a list of all Find Mii II hat locations. If more than 1 hat is listed at a location, you will need to revisit it to get the second or third hat. Each hat is listed in order of appearance.
Find Mii 2 -- Normal Quest Hat Locations
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1. Yoshi Hat, Peach's Crown, Boo Hat
4. Top Hat
6. Pirate Hat
7. Triforce Hat
8. Arwing Hat, Fox Hat
10. Cheese Burger Hat
12. Ninja Hood, Soccer Ball Hat
14. Floral Hat
15. Shy Guy Mask
17. Epona Hat, Cake Hat, Pizza Hat
18. Donkey Kong Hat, Beehive Hat, Red Ribbon
19. Prince Hat, Wario's Cap, Dark Lord Helmet
Find Mii 2 -- Secret Quest Hat Locations
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1. Warp Pipe Hat, Daisy Crown, Yellow Yoshi Hat
5. Panda Hat, Samurai Wig
7. Question Block Hat, Barbara the Bat Wig
8. Tomato Hat, Chef Hat
10. Ice Cream Hat, Straw Hat
12. Lacy Headband, Tiny Top Hat
15. Chomp Hat, Pink Yoshi Hat
17. Penguin Hat, Hibiscus
21. Blooper Hat, Hatchet Hat
22. Sunflower Accessory,
25. Bear Hat, Light-Blue Yoshi Hat
27. Hot Dog Hat, Ramen Hat
29. Football Helmet, Swimming Cap
31. 3Ds Hat, Nes Hat, Famicom Hat
34. Piranha Plant Hat, Magic Hat, Devil Horns
35. Princess' Crown, Waluigi's Cap, Dark Emperor Helmet
Thanks for the image references
Pong20302000!