Yes, there are many options so please ladies don't reach for a baseball hat unless you are going to a baseball game. Hats are always a stylish option especially when you are heading out to brunch, window shopping or sitting enjoying a cappuccino with the girls.
Our tips to finding the right hat:
1. Look for a tight weave hat - this will ensure that sunlight does not pass through and cause sun damage. Some hat materials have been tested to block UVA/UVB rays.
2. Stick with a light colour hat - light colours bounce rays off the hat where as black or dark colours absorb the rays and will cause heat and a sweaty head
3. Material - choose a natural straw, or a combination of natural and synthetic to wick water away. Cotton will only hold water and get heavier and water logged. Eric Javitz uses a material called Squishee ( made from rayon, viscose, nylon and cotton which not only does it breathe but it is packable and doesn't lose its shape.

J.Crew Farrah Straw Fedora

Eric Javitz Squishee Hat

Banana Republic Cartwheel Hat
As for finding the right style of hat for your face shape, this takes time so try many different styles of hats until you find the perfect one for you!