Not like in EU, smoking inside the building is not strict in Japan. Almost all hotels offer smoking rooms and you can still smoke inside the restaurants. There are even smoking rooms inside the stations.
However, smoking outside the building is quite strict. Many municipalities have their own regulations against smoking on streets, especially close to stations and business districts and people who did not obey the regulations must pay the fines. These regulations are introduced due to the cleanliness of the streets and districts, to avoid people throwing cigarettes on the streets. Therefore the municipalities have to create designated smoking areas with ashtrays withing the non-smoking zones.
Smoking at the historical places are also limited too. However, it is not allowed to smoke due to the cleanliness, but rather prevent the fire on the historical buildings. Almost all historical buildings in Japan are made of woods and it is very simple to burn out. The famous Kinkakuji temple was once burnt out due to a arson, a fire set by the apprentice of the temple.
Therefore reasons of no smoking in Japan are different from the ones of Europe. At first, to make the streets clean. Then, to prevent from fire. I assume the reason of no smoking in EU is a health, which Japan does not much care about it.