Car hire is cheap and there is so much to see on Rhodes, as well as good beaches away from the 'drink and be sick' sink-holes. The church at Asklipio is outstanding, and the southern end of the island is not as spoilt by tourism. There is dramatic scenery, forests and mountains, monasteries and roman remains. It is still a real treasure out of the main season.
Visit (or better yet stay in) the Crusader Castle and walk the battlements for 2E and the moat for free. The museum in the Knight's hospital is great with beautiful mosaics in the courtyard and the scale of the of the ward room is incredible.
Our host from Casa Antica, advice us to different restaurants with a special recommandation for Ta Petaladika. Honestly we were wonderfully surprised from the greek food all along our vacation, but it was by far our best 'food moment'. It's located in a nice street from Rhode's old town. An adress known from the locals. The food was awesome, very fresh and tasty with sometimes a kind of modern twist in this authentic cuisine. Definitely a must!
We went to buy a stamps at a main post office and the cashier starting telling us about St Paul the apostle landing on the island near Lindos. Then some Greek mythology. You would not get that at home.