I posted this in response to someone else's question but thought I'd make a separate topic, since it's always a hot one lol
Reiker/Remonte boots Liv 72. I have these in black, and the laces are plain (unlike what is shown in the zappos link). I have not tested them on cobblestones, but have worn them in NYC where I walk quite a bit on varying surfaces. Very comfy and warm, possibly too hot for an 80 degree summer day, but maybe not. Tread seems like it would be quite grippy for cobbles, etc. Water resistant at least, haven't tried plunging into a puddle (yet). I like that they are in the "stylish dressy sneaker" category, so can be casual or paired with nicer pants and you still look cool. Lightweight, not clunky. Very packable, tucked along one side of my carry-on..
Adidas Terrex Free Hiker 2 hiking boots. I got mine online via Dick's Sporting Goods, but Zappo's and others have them as well. I have been hiking locally with these and they are great. Super comfy and warm. Cushy without being mushy. Very grippy (Contintental Tire soles!), very water resistant. The "sock" upper is not for everyone (and there are some versions without it), but I like it and even with my high arch/instep, I don't have much trouble getting into the boot. Also, not too heavy! Lots of different versions, too - Goretex if you want waterproof, various rises - low, mid and high. I would probably wear these on a plane rather than pack them, but we'll see!
I also like Allbirds, although I don't think their new stuff is as good as the originals. And they have the usual durability issue that many "sustainable" shoes have. That said, I think the Trail Runners are a solid choice. Light-weight, they have some water resistance, but also dry quickly. Took these to Sicily, Rome and Sorrento last spring, they did well for me on all surfaces.
I want to add - don't forget good socks. I like the lightweight merino wool socks from Costco, but just got some Dri-Tech socks made by Dickies of all places, and they are fantastic - nice, light-to-medium weight, don't bunch up, dry fast, and come in different styles.