I'm doing something similar in June from Cappadocia to Fetihye. Definitely more convenient than flying and you get to see the countryside and go at your own pace. The only downfall besides cost compared to other options (eg bus) is expectations of Turkish drivers compared to what you're used to in the US. For example, the right of way in a roundabout/traffic circle here belongs to those already in the circle, whereas in Turkey it might be whoever gets in first.

I don't know when you're going, but I'm going doing Ramadan and drivers who are fasting may not be as alert any other time of year, so drive cautiously.