What shoes are good for traveling?

I am going to Europe for a month this summer. We will be hiking various mountains but also dining at nice restaurants, etc. I am looking for one or two pairs of shoes that would be easy to pack, be able to withstand a lot of walking, and look attractive. I am an extreme girly girl and wear a lot of dresses so one of my pairs needs to look good with dresses without cutting off my leg line. They also need to look nice enough for fancy meals, museums, and cathedrals. The other pair needs to be able to handle heavy hiking through the Swiss Alps and various other forests, mountains, etc. Both need to be extremely packable because I am planning to only travel with one backpack.