In my city - DC - I'd assume any guy wearing a non-baseball hat in summer is a tourist. So it doesn't necessarily look out of place in DC, I just would assume you weren't local.
I'm with the Tilley fans -- I have two for boating -- and am especially fond of this one, which seems to fit your parameters:
http://www.tilley.com/us_en/men/hats/tm10b-cotton-mesh.html.