It's a little bit counterintuitive, but here's the pitch: shoes you wear on the bike don't need to be flat, but they DO need to have stiff soles. Some of the worst injuries I've gotten on the bike were when my foot slipped off the pedals while wearing ordinary sneakers or comfortable flats. Conversely I've worn HELLA high heels and never had a problem with them.

My everyday cycling shoes are Keens with the hard rubber sole. They actually don't have the best traction while walking... but hiking traction and biking traction are two utterly different things. And look, I'm not suggesting that you set off for a 25 mile ride in clogs and hot pants! Just remember that stiff soles are better than flexible soles on the bike; and that high heels are not a problem, ladies.