The fastest and most comfortable way of reaching Cappadocia is using the airway. There are two main airports that you can use to reach Cappadocia. One of them is Kayseri Erkilet Airport (ASR) located in Kayseri and nearly one hour driving to the center of Cappadocia region. Turkish Airlines operates several direct (nonstop) flights from Istanbul Atatürk Airport (IST) to Kayseri Erkilet Airport. There are also daily flights from Izmir into Kayseri via Istanbul. It's easy to arrange a transfer or shuttle bus from Kayseri Airport to Cappadocia.
The second one is Nevşehir Kapadokya Airport (NAV), which is located in Gülşehir town of Nevşehir Province. Turkish Airlines operates direct (nonstop) flight from Istanbul Ataturk to Nevsehir Kapadokya twice a day.