Mia goes EVERYWHERE with me. When I first got her I was naive and didn't know they weren't allowed in some places, and we were asked to leave Linens n' Things! Because I know a 1 lb puppy in a carrier can cause SO much damage!
Now I just hide her if we're somewhere she's not supposed to be. The way I see it is she is cleaner and smells better than most children, there is no reason she shouldn't be allowed to go in places! (plus she's even dressed better most of the time!)