About 75km away from Rhodes town is the old town of Monolithos, It is a tiny place with just over 100 inhabitants, There is an amazing medieval Venetian castle and a few tavernas and cafes where you can have a delicious meal. The local produce is cheap and tasty. Try the lamb, olives or locally made honey. There are a few beaches fairly close by, though a bit of a walk.
Fourni beach is a peaceful secluded place, with lots of little coves and caves for exploring. The beach is covered in smooth pebbles and there are a couple of sunbeds and parasols available, though this is more of a beach where you go to get away from it all. Recently a taverna has sprung up, though it is unlikely that this place will ever get overrun with tourists.
If you walk down to the end of the beach where the cliffs are, you will have the place all to yourself. The water here is clean and clear and the waves can get rather big at times. It?s a good idea to bring some of your own supplies if you don't feel like walking all the way back into Monolithos.