A hat! I never, ever go outside without wearing a hat with a peak/bill. It helps with light sensitivity, but it's also a form of "security blanket" but one I'm wearing rather than holding. I feel safe when I'm hiding under a hat while out in public, and vulnerable without one.
My shoulder bag containing my wallet and cards.
My Canon compact digital camera, so that I never miss an interesting picture. I don't have a smartphone to take photos with, so I like to have a camera on me.
Some birdfood pellets in case I run into certain specific crows, magpies and other birds who know me on sight and expect a treat if I'm passing by them. When the crow who knows me jumps down in front of me and I don't have anything to give him, I feel bad even though I know I'll see him again next time, so I always carry something.