Pefkos is an absolutely amazing destination to go to on the island! It has a great beach and wonderful restaurants and coffee shops in the area. The beach is not overcrowded and I personally think its a great place to go with family and kids. There aren't too many organized activities on the beach but it is great for swimming. Here is a great areal view of the beach.
This is one of the most beautiful natural places on the island of Rhodes. In English, it's called Seven Springs, but in Greek it's called Epta Piges. These are natural springs that are open to the public. It is a particularly romantic place and great for couples, especially those on honeymoons. The springs are located in the woods, and have amazing scenery. It's the perfect place for a picnic and to spend the afternoon. I highly recommend that everyone visit!
Monolithos Castle is a stunning castle that was built in the 15th century and remains until this day. This is a birds eye view of the castle so you can get a good idea of what the ruins look like. The Castle is located in the the village of Monolithos which is about a couple of miles from the city. There is no fee to get into the area and walk around and its open pretty much all day!