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On August 17th, every year since the 1300's, there is the Festa Della Madonna Bianca (Festival of the White Madonna) in the neighboring town of Portovenere. This town is most easily accessible by ferry from Riomaggiore, as the bus takes longer. (Advance ferry ticket sales are necessary, just stop by earlier in the day to purchase your tickets).
This is a religious festival for which torches are lit all along the hill atop which the Church of San Pietro sits. Apparently the church sits atop the ancient ruins of a temple dedicated to the goddess Venus, thus giving the town it's name....."Port of Venus," Portovenere.
The torches are lit at sunset allowing those on the approaching ferryboat to see the hill aglow. There are food, craft and clothing vendors. All shops, restaurants and gelaterias stay open late to allow visitors to shop.
It's the same day every year, August 17th, a definite must if you are in Cinque Terre on that date. View this link for a translated website and for a picture of the hill aglow with torchlight. Festa Della Madonna Bianca.