Next to Foinikas you will find the small beach of lupus. The rocky bottom makes this secluded beach ideal for snorkeling. It is not organized. In a tavern there, but just in case you need to care for the necessities.
Walking the beach Vertigo towards Loutro and the footpath E4 will pass the Chapel of the Holy Cross and of course will start next to several small bays which dominate the pebble, sand and rock. There is no organization, and should arrange for all necessary.