Two airports serve central Cappadocia: Kayseri Airport and Nevşehir Airport. Both have several flights daily to/from İstanbul. The main operators are Turkish Airlines (www.turkishairlines.com) and Pegasus Airlines (www.flypgs.com).
Nevşehir Airport was closed for renovation in 2017 but it should be fully operational again by the time you're in Turkey.
Most buses from İstanbul and other western Turkey destinations travel to Cappadocia overnight. At Nevşehir, it's common for the bus to terminate there and passengers to transfer to a bus-company servis (shuttle bus) for the final 20-minute journey to Uçhisar, Göreme, Avanos, Ortahisar or Ürgüp.
The nearest train stations are at Niğde and Kayseri.