An Akubra hat was my hiking and in-town hat for years, until I left it in a restaurant. It looked a lot like Indiana Jones' hat.
These days, I've settled on a Tilley LTM6. Big brim, stays on in the wind, and ventilates almost well enough. Plus, you can wash it after you develop a nice sweat/dust line around the sweatband after a week on the trail.
Tilley now makes one with a neck protector curtain, if you like those (the LTM6C).