What are the best balance exercises for someone with low arches?

I would recommend working with the BOSU trainer, as it will form to the foot if working barefoot. If you do not have access to a BOSU, simple single leg exercises or performing exercises with closed eyes are a wonderful way to train balance and core muscles.

There is a drill we do in martial arts that will help.

It’s called the Four Corner Balance Drill (4CBD). Here is a video http://youtu.be/RpMDLWzLMRg

There is also the towel stretch which will increase flexibility and stability of the foot. Stand with a towel placed underneath your feet. Use your toes to scrunch up the towel and hold the position for 10 to 20 seconds and relax. Straighten out the towel with your toes and repeat the exercise for five sets total.

I use a Reebok Balance Board. It is a safe and fun way to train the foot and ankles.