Although there isn't much in the way of sights or activities in Sobra, there is the quiet rhythm of life in a fishing village. The village stretches along a harbour and contains a few restaurants and a market. Uphill from the village there's a stretch of houses that offer rooms and apartments for rent.
There are no beaches per se but you can easily swim from the rocks along the shore. Although nowhere near as glamorous as Dubrovnik (what is?) the prices are a fraction of those in Croatia's most famous resort. You can even make Sobra a base and take the morning ferry to Dubrovnik for a half-day trip.
Be aware that the ferry port of Sobra is about 2km from the village of Sobra.