I wonder what a Sumerian bar was like. Also, they must have had pretty lax public health rules if they let dogs go in. I can't take my dog to my local coffee shop!
Back then dogs would probably be preferable over the kind of fauna that would impose on you, even in the city. Besides they are a walking hand-towel, are they not.
You're just in the wrong location -- every patio'd coffee shop and bar around me is dog friendly!