I do wear a money belt when I am traveling on my own. I always carry my passport, extra credit and debit cards, and deep storage money in the money belt.
In my purse I carry my "day money" - maybe 30-50E, one CC, my debit card if I am going to the ATM. I have a small amount of toiletries - chapstick, Motrin, tissues, allergy pills, handwipes etc. I have a paper map, my phone, a hand fan (for stuffy museums), sometimes my iPad Mini, metro tickets or pass, sometimes my drivers license, earbuds. You can leave your drivers license if you need to leave something for collateral for a museum audio system altho I had good luck this last time with downloading the museum guides ahead of time to my phone.
This is going to sound totally paranoid but I always carry my passport and money/CCs in case there is some horrible event where I can't get back to my hotel. I want ID and money so that I can make a strategic exit if needed.