Easiest way to rent a car is from the Izmir Airport--they have both international car rentals and Turkish car companies. My experience is that the Turkish companies do not tend to charge a drop off fee if they have an affiliate in the city where you plan to drop the car.
If youlike sandy beaches, Patara wins hands down. Most Mediterranean beaches are pebble beaches, but Patara is a golden sand beach. Not a lot of infrastructure there, but it's a great place to chill out.
If you enjoy ruins, here are some suggestions. Phaselis, along the coast, combines Roman ruins with three beautiful bay beaches. Myra has the best Lycian ruins--the cliffside tombs are particularly interesting. And Demre has the ruined church of St. Nicholas--yes, that Siant Nicholas, so don't miss the incongruous statue of red-suited Santa just outside of town.