Cappadocia is as secure as other parts of Turkey for tourists. Violence is exceedingly uncommon, and it usually has nothing to do with tourists. There is no terrorist danger in Cappadocia. As with any journey, a little common sense will suffice precautions while you are there.
Solo female tourists will find Cappadocia to be a safe place to visit. There is a notion that Turkey is a religious Muslim country in the world. However, this isn’t true. Turkey is a secular state, with no particular rules for women.
You can visit Cappadocia, go to any attractions, and eat and drink whatever you want as a single female traveler.
You don’t have to cover your arms and legs in traditional clothing. You should, however, dress conservatively if you want to visit mosques.
Only during the nighttime should you be in cities and not rural regions. You should also never accept an invitation from someone you don’t recognize. If you follow this advice, you will be safe.