Here is a list of things to do around the Kemer area. I would hope that anyone travelling to this resort town gets a chance to get out of the big hotels and explore the beautiful, natural surrounding areas. Also the culture and historical value of the area.
Phaselis is reached one km after turning left 57km along the Antalya-Kemer highway. This was settled by the Rhodians in the 7th century B.C. and for many years was claimed to be the most important port city of the eastern Lycian seaboard. Phaselis has three harbours the north, the military protected and the south harbour, of which the most important is the later.
Beycik / Tahtali mountain
The Tahtali Aerial Cableway uniquely combines two classic holiday destinations – the sea and the mountains. Mount Tahtali, at 2,365m above sea level, is situated in an attractive and rapidly growing tourist area and provides the region with a new dimension.
It has an altitude of 450 m to 1.000 m at the foothills of Olympos (2.400 m). Therefore, it is in the middle of the Olympos Nature Conservation Park with its pines and cedars and with a breathtaking view from the mountains on one of the most beautiful bays of Turkey.
Cirali / Olympos
Cirali / Olympos is located approx. 80km southwest from Antalya. It is quiet and peaceful village perfect for families, nature lovers and for those wishing to get away from the mass touristic cities or towns.
Once on the beach ( 4kms long -secluded - clean ) you can walk into the entrance of the ancient city of Olympos visiting the ruins located on either side of the creek.
The Chimaera ( ''Yanartas'' - as the locals call it ) is also located at the north end of the village of Cirali. To get the the flames one must either drive 4 kms along the village road to the north end of the village and from there you can walk up the mountain side aprrox 1 km ( 20 mins ) to visit the flames. This spectacular site is best visited at night or at dusk ( bring your flashlight ) There are ruins also found along the path situated closer to flames.
Arykanda is located 26 km. from Turuncova on the Finike-Elmali highway. After leaving the highway it is necessary to walk about 1 km. Arycanda (Arykanda) is a unique Lycian city, built upon five large terraces ascending a mountain slope, and was known for having the most pleasure and entertainment-loving (and debt-ridden) citizens. The city overlooks a magnificent valley and its view makes it one of the most spectacular sites in Lycia.
Simena is a popular Lycian site, situated upon one of the most attractive spots of the Turkish coast. The name "Kekova" is Turkish for "plain of thyme" and describes the region encompassing the island of Kekova, the villages of Kaleköy and Üçağiz and the three ancient towns of Simena, and Tersane (meaning "shipyard", as its bay was the site of an ancient shipyard, with mostly Byzantine ruins).
Demre / Myra
Situated between Finike and Kas Myra used to be a one of the most important of six Lycian cities. Originally a coastal city the gradual build up of silt from the Demre stream has left it stranded several miles away from the sea.. Myra was abandoned after the Arab invasions in the 9th century A.D. The rock tombs and amphitheatre are worth a visit as is St. Nicholas’ church ( Demre ) nearby where the legend of Father Christmas (Santa Claus) is said to have originated.
You may not have the time to visit all of these sites but if you can get the chance to visit a few you will be pleasantly surprized. The sites closest to Kemer are Phaselis, Beycik, and Cirali.
Hope this information is also helpful. Here are all my Travel photos of Turkey that include photos of Cirali and Antalya area. Plus a few other spots worth visiting.