My BF and I spent a day in Rhodes last week and enjoyed wandering around the charming old town. Lots of historic sites and cute shops. Since you asked about restaurants, wanted to alert you to a tourist trap where we had an unfortunate experience and very expensive lunch.
The Castello Family Restaurant & Bar is at the edge of old town near the cruise port. We were looking for a gyro and they featured one on the menu. The proprietor was overly friendly, talked us out of the gyro, and said he’d fix us up with an authentic Greek lunch. We waited 45 minutes and the guy finally delivered a huge platter of grilled mystery meat. Honestly, it all looked and tasted the same. He said it was chicken, beef, lamb, and some sort of sausage. There was enough to feed 6 people. We were hungry but the platter was overwhelming and unappetizing. We ate about 20% of it. The bill was 67.50 euros for the meat platter and 2 cokes. After the fact I checked Trip Advisor and sure enough there were a lot of negative reviews on this tourist trap. Just a heads up, beware.