The closest beach to Skala is Meloi. It's shaded but tends to get crowded. More peaceful is Agriolivadi, in a rocky cove with a couple of tavernas.
Walkers enjoy the dramatic coast around Ano Kambos, the central village of the island at the end of the bus line. The village is surrounded by fertile fields. There are beaches in every direction.
Roads from Skala and Chora go to the beach resort at Grikou. There's a beautiful bay here and lots of watersport opportunties. At the south end of the bay, Kalikatsou Rock may be the hermitage mentioned in the writings of Christodoulos. Inland at Sykamia is the old Roman bath that St John may have used in baptisms.
The road south ends where Patmos is only a few hundred yards across at the Stavros chapel. There's a beach here. Also nearby is the fine white sandy beach at Psili Ammos. To the west is the hot and smelly seaside grotto at Cape Yenoupas, former home to the evil magician.
In Skala, the eating places center around the harbor. The villages have decent eateries and light snacks. The food here is considered better than average.
See our Greece hotels for a complete look at accommodations available on this island.