Diane,
Finding the best footwear for travel has been an ongoing project for me over the last few years. I prefer to travel with only one pair of shoes (the ones I'm wearing), so it's important that I don't have any problems with them during the trip. I also suffer back problems, and I've found these are sometimes partially related to inappropriate footwear.
After a long European trip in the fall of 2006, I learned that I was suffering from Plantar Fasciitis. After trying some "over the counter" solutions (which were useless!), I eventually went to a Podiatrist and was properly fitted for custom Orthotics.
I travelled with Rockport European tour shoes for several years and while these were comfortable, they weren't as robust as I had hoped and started to wear a bit prematurely. It should be noted that these were used only for trips and not for daily wear.
I've been using New Balance walking shoes for daily use, and have found these very comfortable (they were recommended by my Podiatrist).
The current travel shoes I'm using are ECCO Track II (with the Orthotics) and so far these have been fantastic! They're well built, have a Goretex lining and can handle both city walking as well as light trail use. They're also a bit "dressy" if shined up.
I did have a minor issue with the ECCO shoes at first, which I discovered on a trip in January. The left shoe fit too tightly across the top of the foot, and was irritating a nerve as I walked. It was VERY painful! My exceptional local shoe maker "adjusted" them for me, and no further problems since then.
On my last trip to Europe (which I just returned from) I took both the ECCO and New Balance shoes, but I'll probably only take the ECCO in future. I like to travel light, so the extra pair of shoes was a bit cumbersome.
As Charlie (Honolulu/Seattle) mentioned, you might want to check the "Best Walking Shoes" section.
Good luck and happy travels