I’ve gotten several very nice hats from Dorfman Pacific. Some of their Scala hats are very sharp looking.
Straw hats are more classy than boonie hats but boonie hats are cool. And cheap. Buy one of every color, or just the ones that match your Hawaiian shirts. You do wear Hawaiian shirts, don’t you? 
As far as straw hats are concerned, a Panama or fedora have wide brims that cover your ears and neck.
http://www.hats-plus.com/c-194-straw-hats.aspx?pagesize=100
Stratton Hats make a fine summer straw. They supply most of the hats to the various State Police, Troopers, Sheriffs, and Park Service officers. You can add your own hat bands but I would skip the badge.
I bought a Barmah leather hat a couple of months ago on a trip to northern California. Nice wide brim and a pork-pie shaped crown, which makes me look less like a cowboy wanna-be or make street people yell “Hey, INDIANA JONES!” the way a fedora dimpled crown would. And my wife likes it, and she NEVER likes me in hats.
Prices are quite reasonable. http://www.barmahhatsusa.com/
I’m partial to the Aussie style as well, but I went with the full leather, non-vented hat. It’s got a nice sweatband inside, but also holds up well when working in the rain. The one I have is very similar to this. Not only good for yard work, but an excellent hiking hat as well.