Everywhere is different. There's some stores and even malls that allow us to vape in public but some places are strict and look at it as if your smoking. I think it's mainly because people aren't used to them still and some people think it's drugs.
Some places, sure but not everywhere. My work for example treats it like regular analogs, no vaping, no smoking, you must go to the smoking section to vape. It is too new yet!
I vape everywhere unless I am told that I cannot and usually a proprietor of a store will be quick to tell you if you can or can't.