Taxis are available all day and late into the evening. You can normally find them outside Georges taverna on the main road. They don`t cost much either, last year taxi to Lindos for example was 5 euros and a journey around and in Pefkos was 3 euros. Always agree the charge before the journey.
They are reasonably priced. there are 2 ranks in Pefkos, one on the main road through and one on the main beach road near the junction down to the main beach. Both have fares to other towns displayed at the rank, and like you have already been advised just agree any fare not displayed before you start the journey.