I agree with others that you want something in between the cobblestones and your feet, cushioned soles and insoles both work well for me. Leather soles can be fine initially when touring, but after a few hours, I am in trouble.
I have worn black Euro sneakers (AGL) for sight-seeing in Italy with good success. They are sleek, with nice detailing and inconspicuous when warn with pants. There are many brands for good walking shoes, but it is hard to find shoes that both dress up for a fancy meal and let you walk ten miles a day. I know some who discreetly carry their dressier shoes to dinner if it is a bit of walk and then swap them out near the restaurant. Check Ecco, AGL, Born, Naturalizers, Remonte Dorndorf, Reiker, Joseph Seibel, Aerosoles, Sofft, Cole Haan brands as possibilities for comfortable shoes at a variety of price points. Cole Haan puts Nike technology in a lot of their shoes, including dressier ones. Many of their styles aren't right for me, but I find their oxfords usually work. I would focus on comfort as nothing says "tourist" like someone limping from blisters. I also always bring lambswool to stick in pressure points which can develop in comfortable shoes when walking for hours. It really helps, as do blister bandaids.
Your trip sounds great- have fun.
