Zappos.com is a great site that carries all types and brands of shoes. The running shoe fit guide helps determine whether you have a high, medium, or low arch and directs you further to the applicable shoes that they carry.
It depends on your personal foot shape. If you have high arched feet, which you will be able to notice from looking at them, then it is certainly more advised you buy a high arched shoe to accommodate.
New balance has shoes specifically made for people with high arched feet. The shoes have extra padding for the impact made when your feet hit the ground on every stride.
Running shoes are shoes specialized to try and provide comfort and prevent injuries while running. An example of something specific in a running shoe is for the sole of it to be arched to prevent your knees "caving in" which in the long run will make your technique better.
The best running shoes for low arched feet would be a type of underpronators or neutral-cushioned shoes. They offer more of a soffer midsole for the runner and cause less strain on the spine.
Personally I am 6'5", 210lb or so and I have found Brooks Glycerin and Ravenna to fit my feet well (moderate arches, slight pronation, neutral gait.) They also have excellent foot support, which I need being so heavy.
You can find the item in question which is high arch running shoes women online and a couple other websites. You can specifically find high arch running shoes women on amazon.com or modells.
There are no stores that advertise selling high top running shoes. Shoes geared towards running are usually not high top. The most popular running brands are Brooks, Nike and Asics.
Women who have high arches and are looking for running shoes then they should runnersworld.com. They have a wide variety in which shoes to choose from.
High mileage is a term to describe running shoes. The support in these shoes is designed for long distance running. A hiking shoe would be a better shoe for hiking.
Some shoe companies are known for having running shoes with high arches is nike if you have a high arch than you would be a good canidate for these shoes as they are safer.
The most expensive high top shoes that you can purchase are Nike sneakers. They range from $100-$300. You can purchase Nike sneakers and high tops at http://nike.com.
Since running is primarily a continuous, forward motion, rather than stop-and-go like basketball, protecting the ankle isn't as high of a priority. High top running shoes would be better for another sport besides running.