Do I need a visa?+
Greece is in the Schengen area, so short visits fall under the ninety days in any one hundred eighty rule and many passports are visa exempt for that. Everyone else applies to a Greek consulate in advance. Island hopping does not change anything, it is all one country. Verify your nationality on the official Greek consular pages.
Is Greece safe on my own?+
Very. Island life is calm, people are direct and helpful, and solo women travel here in large numbers. Pickpocketing happens in central Athens and on the metro. The bigger practical risks are heat, which is underestimated every summer, scooter rentals on gravel roads, and ferry cancellations that strand you when the wind rises.
Which island should I choose?+
Work backwards from how much silence you want. Paros and Naxos give infrastructure, good food and easy connections with moderate crowds. Amorgos, Folegandros and Ikaria are quieter and harder to reach, which is the point. Crete is large enough to hold both, mountains inland and empty beaches in the southwest. Check the ferry timetable before the accommodation.