If you need a wide brim hat, these are my favorite for infants that need that extra neck protection from the sun. They have an adjustable head drawstring so they can grow with your baby and an adjustable chin strap. Some hats out there have such a huge brim, but this one is the perfect size to protect but not completely take over their face. They come in a waterproof or cotton version and several colors, prints and sizes!
Aqua Dry linked here.
Cotton linked here.