Look for an athletic shoe that has a wider outer sole base than the upper. Asics and New Balance are known for this shape, though I'm sure there are other brands. You also don't want to wear a shoe that is too heavy. New Balance tends to be recommended by physical therapists for the wider sole of the shoe and also because it is generally easy to remove the insole if you use a prescription orthotic insert. You can also go into an athletic shoe store and ask an experienced sales person what shoe is most recommended for balance by physical therapists. If they don't immediately know then try a different store. An experienced sales rep at a shoe store should know what people are being sent to find. Having a good fit is important. Don't worry too much about the appearance to start with. If you are walking with normal use you should need a new pair in 6-8 months. Err on the side of caution on this side too. Better to have a supportive shoe until you get your balance back even if you normally go a while before replacing shoes. Good luck.