My son and I each got a free pair of these from Chrome last year in a facebook promotion.(kursk)

http://www.chromebagsstore.com/shoes.html

They are designed to do just what you are asking for, they do have stiff soles. A lot of people like them, I think they are kind of uncomfortable, but I've never ridden in them as I only ride clipless pedals. Worth checking out. Running shoes are terrible for riding IMHO, along with the flex, the wide heels hit the chainstays and crankarms