Antalya is about 580 km far from Cappadocia and there are several ways to travel to Cappadocia:
Travel from Antalya to Cappadocia by bus
Antalya and Nevşehir are connected by overnight buses that take 9 or 10 hours to complete. From Nevşehir, you can catch a shuttle minibus to your Cappadocian village (service). You might also choose to travel via Konya and see the sites before going to Cappadocia and that way you can divide the driving time into 2 days.
Travel from Antalya to Cappadocia by Plane
Nonstop flights between Antalya and Kayseri (ASR) are offered by Pegasus Air and Sun Express in the summer months. These flights last around an hour. Alternatives include flying via Istanbul on Turkish Airlines or Pegasus Air, with a flight time of around 3.5 hours.
Driving directions from Antalya to Cappadocia
The drive from Antalya to Konya takes between 8 and 9 hours, depending on how you drive, when you stop, and whether you’re going uphill to Konya or downhill to Antalya. It’s a fascinating trip from Antalya to Konya, via ancient Silk Road caravan stations such as the Sultanhanı (great for a meal or an overnight stop), then down through mountainous territory to the Mediterranean Sea. Keep in mind that if you don’t return a rental/hire automobile to the location where you rented it, you will be charged a return fee, which might be hefty.
One of the good ways of traveling between Antalya and Cappadocia is having a private transfer between the cities. You can get more information from here.