You can go with something typical like Nike Air Max sneakers.  Those are probably the best, in my opinion, in terms of comfort and durability.  There are other options, however, if you wanted to go with something less casual.  For example, here is a shoe that’s extremely comfortable but can probably be dressed up a little bit more (This is more for your wife):  http://www.zappos.com/n/p/dp/16240881/c/3.html
 
I know some people like to go for hiking shoes/sandals as well.  Not my kind of thing but they’re supposed to be really comfortable. 
 
Good luck!

Just wear whatever you feel comfortable walking in. My mom got me some “walking shoes” or something for my last trip, but I was wearing them for a month and they never felt right, so I just brought my “normal” shoes and they worked just fine.

I agree with Feicht, bring what is comfortable. My first backpack experience I traveled with hikers. Ugh! I bought a water runners last year – not crocs, actual runners by Salomon. They are almost all mesh and the heel was built to be folded over if you want. It was the best travel shoe I’ve ever had – nice and breathable. You will want something with cushioning as pavement can be hard on your joints, etc if you plan on doing a lot of walking. I always bring a pair of sport type sandals (Tevas). Some people just bring flip flops but I find if you get good sport sandles, your feet will thank you! I’ve heard that crocs are very comfy too as an alternative to sandals. I prefer to avoid leather, but you can get leather travel sandals, which would give you a more dress up alternative too.  If you feel like going out one night, you can always also buy a nice fairly cheap pair of shoes there. Last year I bought some espadrilles for 15 Euros or something like that. 

Since you’ll be going in September closed toed walking shoes are your best option.  If you want to blend in avoid tennis shoes and hiking boots and get a darker colored shoe.  Merrell makes smart looking walking shoes, you could even get away with the Jungle Moc in a dark color, other brands are Rockport, Ecco, Geox, Born (http://www.onlinesho…)

For Women my favorites are Danskos, Merrell also has great shoes for women, Clarks, Mephisto, Naot, Royal Elastics, Diesel.
Zappos has a great selection and there are usually user reviews of the shoes which is helpful. 

Good idea to buy the shoes well in advance to break them in. Good luck!

New Balance brown sneakers. Comfortable, and look decent enough to wear into some clubs even.