Athletic shoes for high arches

Go to a local running store and get properly fitted. Not a sporting goods store but a running specialty store. You will pay more for shoes locally than you could get them for online but a good fitting is worth it. Then get your next pair online for less.

Or, I order from www.roadrunnersports.com all the time. They give you a return period - you can try the shoes out, even outside, and return them if they don't work for you.