I can't get any sun either and I recommend this type: http://www.amazon.com/HDE-Women-Packabl ... able+visor
I'm not sure if the one I have is the exact one in the link, but with that style I can keep one rolled up in my bag and pull it out whenever I need it. Also, it's so hot to have a real hat on in the city where I live in the summer. The open top aspect of the visor is much cooler. It's not the most stylish of hats, but being too hot/having a lot of hair that doesn't fit under a hat makes me deal. The one I have connects with Velcro so the size is adjustable.
I also have had luck layering a base layer of natural block with zinc and a chemical-based on top. This zinc based block has been a godsend for me as someone with acne prone skin (it goes on dry). I am not sure if it is vegan:http://www.amazon.com/gp/product/B006HI ... UTF8&psc=1