Most foot doctors recommend New Balance, and I used them for YEARS- just switched to Asics in the last 3 years because I started running. MUCH better in my opinion. They are stable and have a lot of cushioning. Walking around Disney this last trip was much nicer in them. I have found that you get what you pay for with cushioning.
I know the stares from people well. We have an autistic son, and we have a GAC, and we have gotton stares, and comments like- nobody looks handicapped to me... We know why we have it, and I have gotton to the point where I just let it roll off.
See the part of me that is evil would want to look at those people and say..
"Actually you don't look handicapped either - but to be so ignorant as to make that comment to a family with an autistic child, you must not have the mental capacity of an adult. Poor thing!"
Funny? I think so.
Anyway - the key to stabilizing your back while walking comes in motion control shoes. These shoes have a hard plastic shank at the bottom of the sole that do not allow the foot to flex to the fullest extent. I know what you are thinking - that sounds awful! However, if you have own shoes that you can easily fold in half from heel to toe - you will understand. Those shoes don't provide enough support to any part of your foot to stabilize your foot, let alone your back!
I know opinions vary widely on what a shoe should and shouldn't do - especially with the whole barefoot shoe craze right now... and the resulting increase in foot injuries - it seems to make sense that the type of shoe you wear should reflect your body size, build, weight, and carriage.
Then, there are the shoes that make your body slant forward due to a wedge shaped sole block made up of foam and other materials. Who thought that was a good idea?
Anyway - you have to take into consideration the design and construction of the shoe. Some of the best shoes that I've purchased ended up being horribly uncomfortable. Some of the shoes that I bough just because they were priced right ended up being the best!
Case in point, the dress shoes that I favor right now were under $30.00 - but they do not hurt my feet, they support my arches, and they don't have a heel! (I'm not talking about a 'high heel' - I'm a guy! HAHA) They aren't wedge shaped under the heel, with a weak stretch between the ball of the foot and the heel.
I've had good luck with New Balance for tennis shoes - and Clarks/Bostonians in dress shoes.
Ask about motion control shoes - New Balance makes 2-3 types - and they also sell motion control insoles.