Pfft. Turtleneck. Or more realistically, one of them “buff” things. Basically turns whatever you’re wearing into a turtleneck.

Hats are hot and stuffy, I’ve found. I carry an umbrella as a parasol unless I’m biking or need both hands. Then it’s the Buff.

Also, a backwards hat to protect from the sun realistically offers dubious protection unless you are always walking directly away from the sun.