I have high arches, and no sneakers on the rack have had much support. After having a wicked bout of plantar fasciitis, I decided that enough was enough. I bought some KURU Sneakers. I bought the Quantum Womens for my every day sneakers. They're $120, but they're worth every penny IMHO.
What I like about them is that you wear them around your house for a few hours at a time and let the shoe mold to your feet. Once they do, it's absolutely incredible the amount of pain that went away by having supportive shoes.
That being said, I did wear one pair out and I got a blister on my 4-day walking trip through Washington DC museums. However, that same pair got me through a 4-day trip to Disney World in February with zero blisters. (So, I solved the problem and bought my next pair to wear for my September trip.)
I actually bought a pair of the KURU KIVI clogs to wear for work, too, because my work clogs were absolute garbage (and probably contributed to the plantar fasciitis and heel pain.) I just threw my old shoes in the garbage when I got them and wore them to work the next day. They're $135 and worth every penny spent on them.
KURU makes several other styles (flats, sandals, flip flops) but my feet are between 11-12, and I wear a 12 in KURU sneakers, so I haven't tested the Sandals yet.
I also live in Crocs flip flops all summer. I have worn them to
Disneyland with no issues. I find there's a lot of cushion and support. I wear the ones with a leather thong and not the Crocs foam ones. If I were to buy the foam thong sandals, I'd probably put moleskin on the upper thong part that touches my foot.
I have a pair of Tevas, but they tend to stretch my arch out too much, and after a while, it's exhausting on my feet.
TL; DR version:
If you need/like arch supports:
Sneakers/Clogs/Shoes with Arch Supports: Kurus
Sandals: Crocs (and Kuru if your feet are small enough.)