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More than 20% of Italians are smokers and that includes teenagers. Although the government has recently tried to introduce some new laws preventing kids under 18 from buying cigarettes, the laws can often be broken especially considering most of smokers under the age of 18 get cigarettes from their parents at home. In most of cases teenagers smoke because someone older in their family does. So don't be scandalized if you see kids around the age of 15 smoking.
As a matter of fact, in Italy it is only forbidden to smoke inside public spaces: cinemas, restaurants, clubs. There are no smoke-free areas outside or near buldings (in case of bad wheater you will always find a small group of people standing right be the entrance of public spaces smoking, just take a deep breath and say excuse me when walking in or out). That includes outdoor areas of restaurants; tables in squares, courtyards, gardens and porches are considered "outside".
Although dining by Venice Lagoon or in any Piazza in Rome is very romantic and a must if on a trip during summer, think about it if you want your kids not to be near smoke. You won't be able to complain if you are at an outside table and if you do, you'll kindly be offered a table in the inside of the restaurant. Also consider Italy has tourists from all over the world and some European countries still allow smoking inside public spaces, so these people are already feeling restricted, compared to what they are used to.
Also consider it a very kind offer (and act as you are appreciating it) if someone local offers you a cigarette when talking to you. Italians offering to share something is a way to show they are interested in what you are saying and want you to stop for some more conversation. Just kindly answer you don't smoke but will love to sit with the person and have a coffee.