There is a little beach off the small fishing village of Diafani that you could swim in, but for a more secluded experience head to nearby Vananta (pronounced Vananda). Better done by boat than road from Pigadia.
Megali Ammoopi is perfect for families with children thanks to its shallow waters. Nearby is Votsalakia, a pebbly beach with fantastic water. These are popular beaches with restaurants, cafés, hotels, etc.
Here’s a well-organized beach near the big village of Arkasa on the western side of the island, 15 km north of Pigadia. White sand, shallow waters and delicious little restaurants (tavernas) serving seafood and local cuisine.
These three sandy beaches near Pigadia, the capital of Karpathos, offer clean waters, different watersports, good food and sea-side restaurants. They are most popular and happening, so not ideal for those seeking privacy.
In the bay of Lefkos on the central western side of the island there are 3 beaches that can delight curious travelers. Gialou Horafi has umbrellas, while Panagias which is smaller and quieter does not.