Cappadocia is on Turkish time, UTC+3, like the rest of the country. What changes from city to city is the daylight.
Turkey keeps one time zone across roughly 1,600 km, so the clock in Cappadocia matches Istanbul exactly while the sun rises at a different moment. The figures above are calculated for Cappadocia's own coordinates and update as the date changes.
Cappadocia is a region rather than a city, centred on the towns of Göreme, Ürgüp and Uçhisar. Volcanic tuff eroded into the rock spires locally called fairy chimneys, and people have been carving houses, churches and whole cities into that soft rock for thousands of years.
The balloons launch at first light, which is the practical reason to know the exact sunrise time here. In midsummer that means being awake before four in the morning.
Cappadocia is in the Central Anatolia region of Turkey.