We're headed to Greece in a couple weeks (our first time there), and will begin our trip with 3 full days (4 nights) on Rhodes. With three full days, I know we will not see everything there is, but I'm hoping Rhodes will serve as a decent introduction to the Dodecanese and Greek islands generally. (After Rhodes we will head to Crete for 12 days; we finish with a couple days on Santorini - not my personal preference, but non-negotiable with my spouse, and I'll be OK with that). Most of our trip will be around Crete, and I think that'll generally hit the sweet spot for us (we will have a car on Crete as well; not sure yet about Santorini, perhaps we will rent a car for one day there).
I know Rhodes town gets crowded with cruise ship passengers and has no shortage of overtourism, but it still seems worth a visit. I'm assuming we will want to spend 1 (maybe 2?) of our 3 days in/around Rhodes old town itself; we have a nice place to stay deep in the old town, so we will wander and explore and do our best to avoid the worst of the scrum when we can. I know that cars are verboten there and even parking outside the center is challenging. But I also know I'm going to want to get out and explore some of the rest of the island a bit on at least one day, maybe two, so I'm planning to rent a car for that. Places that look intriguing and potentially worth a stop include maybe Afándou Bay, Stegná, Líndhos - well, I guess the whole coast, especially once you get away from the major development near the old town and beyond. So we will probably spend a day circumnavigating the island, hugging the coast for the most part, maybe poking around the interior a bit if we have time.
I'm looking for any suggestions to help me allocate our time, places worth stopping at as we explore the island. Scenery, dramatic landscapes, historic sites, views, nice beaches (prefer them as un-crowded as possible, though I know Rhodes has no shortage of tourist development). Since we will be there in the second half of September, I'm hoping the worst of peak-season crowding may have passed, but I know it will still be at least somewhat crowded most places. I'm assuming the sea will be warm enough for swimming, we will take a dip now and then (we will be bringing our compact "travel snorkel" gear; we don't spend time laying in the sun).
With three days, how would you split your time between Rhodes town, and rest of the island? Any (pleasant) surprises outside of town you can recommend that we might not otherwise stumble on? Places not to miss (and places to avoid like the plague)?
Thanks for any insights you can share.