Rhodes is quite a big island, if I'm not mistaken, it's the fourth biggest in Greece after Crete, Evia and Lesbos (haven't visited neither one of them, but I'm thinking about going to Crete this summer) and as you can imagine it will be harsh to travel from one side of the island to the other. Here my top picks that can help you with choosing your accommodation if you ever decide to visit Rhodes.
Saint Paul's Beach - situated near Lindos, I rate this beach at first place on several different reasons. Let me first tell though that there is no free zone, if you go to this beach you'll need to rent a sunbed. The good thing is that they're not that expensive, or at least in May they weren't. The price for a sunbed was 10 euro and there is even a better offer for couples. You can rent this big swing with two sunbeds on it on the first line of the beach for 30 euro. The itself is located in a small bay therefore there almost no waves, the water is very calm. On one side of the beach, up in the hills is located Lindos Acropolis of which you have a splended view. And the last reason I rated this beach on first place was the food. Just a few feet from the beach there is a beach bar/tavern... or more like a restaurant that served amazing food.
The beach is located in the bay on the bottom of the photo
Tsabika Beach Gorgona - situated in the middle between Lindos and Rhodes, on about 30, 35 kilometers from both cities is located Tsabika beach, my second pick. Easily accessible by car the beach has very long beach line and has as well as paid and free zone. Consisting of a very nice, silky soft sand, as I like to call it, we stayed on the free zone. The sea was not nearly as calm as the one at Paul's bay, the Tsabika is not located in bay exactly and has a lot more exposures to the open sea. On both sides of the beach there some rock formatins that a perfect instagramable locations and I highly recommend to check them out. Other than that there are many beach bars where can grab a bite to eat or just have a cocktail or a coffee.
Anthony Quinn Bay - just a 15 kilometers drive from Rhodes old is located Anthony Quinn bay, my third pick. The beach is fairly little and it's full of sunbeds, there is almost no space for a free zone, so if you're not ok with paying 5 euro for sunbed make sure you go there as early as possible to find a spot. Again a very beautiful and picturesque location. As it was at Paul's bay vert calm water with almost no waves, a perfect place to chill. There is a tavern on the beach which served amazing food for a very reasonable price, so don't worry about staying hungry or getting broke.
Prasonisi Kite Beach - ah, the place where the two seas meet! A huge beach line on both sea and a lot of wind were expecting us there, I mention again this was in May which is still considered off season. The beach has a free and a paid zone, it consists of silky soft sand so we again stayed on free zone, we didn't neede sunbeds. As you can guess by the name water sports are offered here as Kite and many more. There is tavern to grab a bite to eat or just get a coffee or something else do drink. The only big CON a find on this place is that it's very far from most of the cities. It's situated on the eastmost point of the island.
Beach of Lindos - my last pick for this list, Beach of Lindos. As you can guess by the name, it's located in Lindos. A big beach line with free and paid zone. Again located in a bay, not as small as the one at Saint Paul's Bay but the water is farely calm. Many beach bars and taverns can be found there. We didn't spend a whole day there, we just checked in out on our way back from Saint Paul's Bay, but it deserved to be on our list. If you have more time definitely check it out!