Honestly nothing beats having your own bike there, you just point the front wheel wherever looks interesting and go, no waiting around for dolmus timetables or haggling with cab drivers who spotted a tourist from a mile away. The coast road stretching out towards Gazipasa is a gorgeous ride with the sea on one side and mountains creeping up on the other. Plenty of places let you rent a motorbike right in Alanya itself, just browse what is listed here
https://getrentacar.com/en-US/motorcycle-rental/turkey-alanya .