These are great options for women who workout indoors and outdoors (training and running). If you have flat feet, these recommendations are great for you. Keep an eye out for sales that drop every now and then on these sites.
Great for all around gym wear. If you have flat feet, these will do just fine.
Nike V2K Run
Lighter than the Metcon 9!
Nike Metcon 10 Women's Workout Shoes
Stylish and comfy. Great for flat feet.
NEW BALANCE 530 Womens Shoes - WHITE/NAVY | Tillys
I use these shoes everyday and have been for over 1 year. They are comfy and I've worked out in them comfortably indoors and outdoors.