On my second visit to Piran I had a stroll to the Punta lighthouse. It is located on the tip of the Piran peninsula. Beyond the lighthouse there is a church formerly consacrated to Saint Clement. In the 17th century it was renamed as Our Lady of Health because of the plague that propagated throughout Istria. This church was first mentioned in the 13th century.
At the lighthouse area there is a good choice of restaurants and a concrete beach.
Besides the Tartini Square this is my favourite part of Piran.
There are several cafes, old houses, beaches...
AND: There is the best ice-cream in Piran :-)