It appears that in Japan, there is an old custom called Uchimizu. The name is a combination of words "road" and "water". The essence of it is moisturizing small parts of populated areas like sidewalks, streets, parks, gardens. A very nice diagram explaining how Uchimizu is performed can be found on this site.
Apart from being a traditional and cultural thing, various sources (Wikipedia) claim that it helps reduce the heat in the surrounding area, but don't say by how much exactly.
They also say that it prevents dust particles from spreading, but this is a more obvious part of Uchimizu, as watering sandy ground should prevent the wet sand particles from flying around. I'm more interested in the cooling effect of Uchimizu here.
Let's say we have enough people watering everything in a small city, enough to make 1/2 of all the outside surfaces wet at all times. Potential harm to structures aside, by how much degrees Celcius will the average temperature in that city decrease? Let 30°C be the average summer temperature during the day.
What about watering only the area in immediate proximity? For example, everything around your house. Will that help reduce the summer heat?