It looks like I was wrong. Tonight, day two of the ban, I was walking around the city with Bella the dog in tow. Bella is a leisurely walker - she likes to stop and sniff - so I had plenty of time to glance in the cafes and bars as we passed.
In smaller local bars, the picture was mixed. Some places had cleared the ashtrays off the tables; in others the customers were puffing away as normal. In more central areas, the change was more noticeable. Most places had removed the ashtrays; one had placed a large no-smoking sign on the entrance; another had multiple signs on the walls; a third had individual no-smoking signs on all the tables.
The timing of the ban has been helpful. Since the days are hot and the evenings are warm, many people are sitting outside where smoking is still permitted. Also, the enclosed patios that front many premises are being treated as an outdoor rather than an indoor space, and therefore not subject to the restrictions. I'm not sure whether this is the legal position or an interpretation by the owners of bars.
At some point this week I plan to take a walk round and visit a dozen local bars and cafes - purely in the interests of research - without a dog in tow, to get a better idea of how things are working out.