One of my favorite places to recommend is Canfora Sandals, on Capri. They have been around for many years — they even created the sandals Jackie Kennedy wore. They will measure your foot and create custom sandals while you wait. Amazing. You can order online, but the personal service is really special.
Canfora Sandals, 3 Via Camerelle; 011-39-081-837-0487, http://www.canfora.com