I spent a week in Siena and Florence and had no problems whatsoever. I just carried a regular purse or larger leather carry all, slung cross ways across my chest. I didn't feel unsafe anywhere, at least not more than I would in any other big city. Of course, in Siena, we were visiting my son who was studying there, so a lot of the time he was with us, translating for us, speaking for us, and leading us (talk about a role reversal). We even managed to rent bikes, get lost, and climb to the top of a mountain that is part of the Giro. That's the only time I ever saw my husband get off the bike and walk, mostly because we had no idea how long the climb was (we were actually 3 km from the summit. We flagged down a tri athlete from France who was bombing down the mountain and somehow, with no English, we figured out where we were).
I hope no one takes this the wrong way, but I have found that a good way to avoid trouble in Europe is to dress like a European... no sneakers, fanny pack, baseball cap, etc. I have a couple of pairs of very cool looking walking shoes, that I bought in Vienna and Prague that I wear on all of my trips.