I have foot issues, so this is a major concern for me. I wear a combination of shoes, depending on the weather while I'm there (just got back from there and needed closed toe shoes just for warmth).
I wear - Chacos Z2 style, Keen Presidio, Papillio (birkenstock) clogs (Frankfurt are my latest faves), Birkenstock rubber/eva flip flops (even they have to have arch support), and one pair of Crocs Mary Janes. I just can't stand the look of the regular crocs on me - I see them on other people, and like them fine, but I have bigger feet, and just feel like I have duck feet in them. I got the Mary Janes, but they aren't supportive enough for all day - I can wear them for about a half day before my feet are done with them.
For me, the best sneakers are Asics. The pair I have now I have walked about 100 miles in, plus done some gym time and they are holding up very well. They are light, easy to clean and have fantastic support.
Like everyone - wear something you have broken in, bring more than one pair of whatever you decide on, and know that at some point your feet will probably get wet.
Also - if you wear closed toe shoes/sneakers, pay as much attention to your socks as anything... you can take a fabulous sneaker and it won't be wearable because of the wrong sock!
Good luck!!!