Yes. You can either fly to Kayseri (75km to Goreme) or Nevsehir (45km to Goreme) airports. There are several direct flights to Kayseri and 3 flight to Nevsehir everyday, operated by Turkish Airlines. Pegasus Airlines also flies everyday to Kayseri. Their flights are from Sabiha Gokcen airport, located on the Asian side of Istanbul. There are also 3 direct flights a week (on Monday, Wednesday and Saturday) between Cappadocia and Izmir. Sun Express Airlines operates Izmir-Kayseri flights.
There are buses from all major cities of Turkey to Goreme or Nevsehir. Pay attention to buy your ticket to Goreme, not Nevsehir. Some travel agencies in Nevsehir bus station will claim that they will transfer you to Goreme free, but will hassle you a lot for selling tours and leave there if you don't buy one. Major companies like Metro and Nevsehirliler will have service buses from Nevsehir to Goreme bus station. Just like the flight tickets
If you have a car or rented one, you can enjoy the scenery of Turkey while driving to Goreme. Drive via following cities: Istanbul to Goreme: Istanbul, Bolu, Eskisehir, Ankara, Aksaray, Nevsehir, Uchisar, Goreme Ankara to Goreme: Ankara, Aksaray, Nevsehir, Uchisar, Goreme Izmir to Goreme: Izmir, Usak, Afyon, Konya, Aksaray, Nevsehir, Uchisar, Goreme Antalya to Goreme: Antalya, Akseki, Konya, Aksaray, Nevsehir, Uchisar, Goreme The chart under the page, will give you an idea about the distances to Goreme.