From easiest/quickest to longest...
You can fly from istanbul to nevsehir. This is about 1hr flight. Nevsehir-capadoccia is just 20 min by bus.
Flights to nevsehir is not that frequent, therefore You can fly from istanbul to kayseri and then take a bus to capadoccia. This bus will takes approx1 hr and the same for your flight.
Alternatively you can take a bus directly from istanbul to capadoccia and this is approx 750km distance. over 6 years ago