I just completed the most ridiculously thorough research to find the best pair of sandals for my trip in two weeks - over the course of a month I ordered 20 pairs of sandals from Zappos and also went to a local shoe store for a fitting. Like you, I was set on wearing sandals (rather than sneakers) because of the heat.
In the end, I went with Chaco's - great arch support, sturdy, comfortable, and can handle getting wet. I also bought a pair of Keen's Venice H2 so that I can rotate the two pairs (we are doing 5 days). The very knowledgeable salesperson at the local shoe store I went to told me that the Keen Venice sandals have the most arch support of all the Keen's (in general, I found that Keen's didn't have enough support for my high arches, but these seem to).
I tried Teva's but they didn't offer me enough support. (I'm a runner who has occasionally struggled with plantar fasciitis so arch support is a big must for me - others might find Teva's to be just fine).
I also really like Birks, but wanted something a little better for water. There are some Birks (sold under the Birki's line) that are water shoes.
I would highly recommend shopping on Zappos so that you can try several pairs and easily send back what doesn't work. Good luck!