Gazipaşa sits east of Alanya and exists to serve this stretch of coast. If your flight lands here rather than Antalya, the transfer is a third of the distance: 40 km against 128, and around 45 minutes against nearly two hours.
The road runs along the coast the whole way, climbing over headlands and dropping back to sea level between them. It is scenic and slower per kilometre than a motorway, which is why 40 km takes 45 minutes rather than half an hour.
Mahmutlar and Kargıcak sit between the airport and Alanya centre, so hotels there are reached before town. If you are staying west of the centre, past the castle, add roughly fifteen minutes to the figure above.
Gazipaşa handles fewer flights than Antalya. When both are options for the same trip, the shorter transfer here is usually worth a less convenient departure time.