Hats and Glasses
Since the sun is so powerful, just wearing sunscreen is not enough. Remember, UV Rays, (both A & B) can cause some very serious damage to the corneas and retinas in your eyes. Always have sunglasses on that are dark enough to block the sun - and that have a SPF protection label on them upon purchase. If your face burns easily, purchase a sun hat. A wide brim and light weight sun hat will keep your face shady, and keep your whole body cooler.
If you just want to spend some time outdoors, and are not intentionally trying to get a tan, make sure you wear protective clothing. You don't have to be hot and sweaty to be covered up and protected from the sun. Linen pants and shirts are very porous and allow breezes to blow through to keep you cool. Light colors conduct heat far less than dark colors, so stick with whites, tans, and khakis.