I normally carry either a moneybelt, neck wallet or leg wallet and try never to show it in public. I keep my passport, credit cards, extra cash and any other valuables I absolutely don't want to lose in it.
I've been also carrying a Civita daypack on tour days for low value necessities such as water bottle, umbrella, sweater, picnic stuff, sun screen, groceries, etc.
I'm thinking of leaving the daypack at home this trip because it may be more worry than it's worth when touring, especially getting through security and storing it at sights.
The question is what am I to do with my moneybelt? Leave it in place or produce it for security? What's are you doing with those things you really don't want to lose? What are you taking with you at all times?