For both walking around and driving, I got a pair of these New Balance Foam Arishi "running" shoes. The soles look thick/tall in this pic, but most of what you're seeing is where it wraps up on the edges. They are actually very light, with thin and flexible soles that give great feel on the pedals and good comfort. I'm not sure they're actually great for running, but they'd be good for working at a job where you're on your feet all day. I don't have special driving shoes: these are my autocross and track shoes, as well as my casual walking-around shoes.
I also have a pair of dedicated training shoes that I use at the gym. They are very stiff and have lots of support, so they're great for weight training and other active things like that. But they are terrible for driving: very little feel for the pedals at all.