Different from most other replies: for my husband we bought ankle-high boots similar to the Propet Shield Worker or Propet Blizzard mid-lace. (The exact style probably isn't available anymore as this was a few years ago.)
They are very lightweight and have good sole traction, and the man-made material is waterproof. They look "normal" enough to wear with dress trousers and a tweed sport coat for dinner in a nice restaurant, and don't make him stand out as a tourist. (One of my pet peeves is American tourists wearing obvious mountain gear ambling through downtown city streets.)
To choose these we ordered four different boot styles, if I remember correctly, and he kept the pair that felt best on his feet. Comfort is really the paramount consideration for travel boots since you will be wearing them for long hours.
His only other travel footwear is a pair of sturdy slippers from Orvis with a convertible heel so they fold flat for packing. The slippers serve to give feet a rest in the evening without having to walk around in stocking feet (or barefoot) on hotel carpet/floors, and they provide enough support to wear down to the lobby to get a newspaper or whatever.
Since OP is looking for "all around shoes," I really thought these were a good answer.