The trouble with riding in sunny weather with your short sleeve cycling jersey is that farmer's tan you'll inevitably end up walking around with well into the fall months. Try buying a sleeveless jersey instead. You'll stay cool and fashionable at the same time. Many companies (like Fox Clothing) make excellent racing & performance gear as well as sportswear.
*Ladies, if you'd like to quickly put on a dressier look over your cycling clothes, find a wrap around skirt make of stretch materials (a dance shop will have one). You can pack it up and take it along (it won't wrinkle).