Dogs definitely aren't allowed on public transit. Guide dogs are the exception, of course, but that's because they are given the travel rights of humans and can go anywhere that their owner does.
Beyond that, they aren't allowed in stores or restaurants generally. When I lived in Vancouver, I was amazed to see that people took their dogs out everywhere and it wasn't uncommon to see them sitting outside with their owners at cafes and restaurants. Every place I've lived in the States, though, doesn't allow that. You might occasionally see people sneak small ones in their bags into grocery stores or dorm rooms, but it's usually frowned upon.
