BTW, Sarikinarya is a she not a he.
1) Aspendos Theater: A bit east of Antalya so perhaps off your route. This ancient theater has enjoyed constant use and maintenance since it was constructed so it is in amazing condition and perhaps the best example of a free-standing Roman-style theater in the world.
2) Sunken City of Kekova and island of the same name: Beside the modern village of Kaleüçağız about 10 km east of Kaş. Besides the ruins, the sea is especially beautiful. Swimming/kayaking/diving is now allowed away from the ruins.
3) Demre (Myra): A few km further east of Kekova. Home of Santa Claus for years and some outstanding cliff-cut tombs.
4) Kaputaş Beach: About 15 km west of Kaş near the west end of the most beautiful seaside drive in Turkey. This little beach is incredibly beautiful. Only some road-side parking and no services save a Turkish family that brings cold drinks/fruit/umbrellas/etc. down the cliff-side staircases. The reasonably frequent buses along that road will drop you off and pick you up.
5) Patara Beach: About 10 km west of Kalkan. This is a long, sandy beach that is protected from development. There is only one service area near the eastern end of the beach just past the village of Gelemiş. Even a short walk from the service area will find you nearly alone. There is even a decent ancient city to explore as well.
6) Xanthos: Ancient city a few km north of Patara. Great views, reasonable ruins and nearly deserted, but may be difficult to access via public transportation.
7) Paragliding at Ölüdeniz: A few km SE of Fethiye. Ölüdeniz is utterly overrun with package holiday goers but paragliding there is awesome! There is also paragliding in Kaş.