Definitely not for most folks, but because I regularly spend up to a week at a time 'off the bike' during tours exploring cities along the way, I travel with these two items:
1) Keen Austin leather bike shoes with SPD clips. Keen has a giant toe box which is comfortable with my (aging) feet. Off the bike they could pass as casual-dress shoes and are comfortable for all day walking. I've never had problems with my feet feeling hot in them, although if you are prone to that issue you might want to look into sandals as others suggest.
2) Ecco sandals. Here again, probably heavier than most folks will want, but excellent support for all day walking. As another poster mentioned, with/wiithout socks gives you two different personas.
Also, I ride with reversible pedals which give more flexibility in footwear and foot position. (tip: If you have any history of plantar fasciitis it may be useful to not always have to be clipped in.)