I have taken mine in all sorts of places... TJ Maxx, Homegoods, clothing stores.
Here (NYC) dogs are allowed pretty much anywhere as long as there is no food, I usually pick mine up when I walk in and I have had more then one employee stop me and tell me "they are fine to just walk around".
As long as there is no food, I usually will just go in and if I get thrown out, I'm okay with that
I have been thrown out of a few places upstate when I visit my parents and really most people are pretty nice about it, they just come up and politely say that dogs are not allowed and I leave... its not a big deal!