You might have a look at this online shop:
http://www.herrenausstatter.de/0601_...=Markenauswahl
The selection under "Filz & Strohüte" -> "Stroh und Papierhüte" is appropriate for (big) cities like Düsseldorf, Hamburg, Frankfurt and even Munich (
) and in Austria and Switzerland.
Regaring how to dress:
If you wear a hat like mentioned in the shop above, it should be fit to the rest of your wardrobe, i.e. not shorts, white socks, shirt and a hat. Depending on the style it should at least be chino, shirts and appropriate shoes (not running shoes and no sandals).
If you wear a hat as a German, you are somehow sophisticated, a little bit upscale and care for your wardrobe. Think about the clothing for a casual friday in an office. There is no need for long blazer, sleeves (unless you wear a tie) and even a polo shirt (without big oversized logo of someone playing polo on a horse covering the whole front of the shirt
of course) would be okay.
Your wardrobe could be more stylish, if you use the hat as a fashion statement. But then you should be the person able to wear this kind of clothes.
Personally, I think a baseball cap is not a appropriate type to cover your head, if you are an educated German and older as 18 - but that might be just my own point of view.
Here are a few examples of (more stylish) outfits where I think a hat would be possible to add:
