I wear hats most times, now that I get sunburned on the top of my head! It works out OK for me, as I like to wear hats anyway.

For summer, I suggest a driving-style cap or irish flat cap made from a light weight material like cotton, linen, or silk. There are many varieties of this style. You can see some examples in linen here:

http://www.hartfordyork.com/category/linen-caps

Those include some really top makers, like Borsalino, but you can find cheaper versions too. The Tilley hats that were suggested previously also look really good!