So, started to look into this a bit more.
Sites in the proximity:
* Rhodes City, Greece
* Xanthos-Letoon, Turkey
* Ancient Greek Theaters, Greece: Lindos
* Ancient Towers of the Aegean Sea, Greece: Ro, Strongyli, Kastellorizo
* Ancient Cities of Lycian Civilization, Turkey: Patara, Tlos, Pinara
* Kaunos, Turkey
* Kekova, Turkey
* St. Nicholas Church, Turkey
For the tentative ones we should pick the best one where there is more than option. The towers look funny.
Ferries (I think there are more operators than this, please check).
The ferry Rhodes<>Fethiye runs 9:00-10:30h and returns at 16:30h.
The ferry Rhodes<>Marmaris runs 9:00-10:00h and returns at 17:00h.
* Friday Arrival Rhodes. Rhodes City is open all night.
* Saturday Excursion Turkey (Ferry 9 a.m, return 16:30h): Xanthos and one/the best of the Lyician Cities
* Sunday Excursion Lindos and Siteseeing Rhodes. Then heading home.
Itinerary 2 (a fun one):
* 07:00-07:40 Flight to Kasterlorizo (70).
* 10:00-11:00: Watertaxi (20min) to Kas. Normal ferries will break the schedule.
* 11:00-12:30: Kas -> Xanthos
* 14:30-15:30: Xanthos -> Lycian
* 17:00-18:00: Lycian -> Fethiye
Sunday: First ferry back to Rhodes.
* Personally, I think I will stay in Turkey on Saturday and continue along the West coast back to Istanbul in a week for siteseeing.
* I think there are more ferry operators. It would really help to get an earlier ferry to Turkey and a later ferry back. We could then squeeze in Marmaris / Kaunos which looks interesting. Or one of the towers.