Travelling solo is a unique experience, a true lesson of life. The things you learn about yourself when travelling alone are numerous and precious. Together with your best friend, a mate, who will never leave you, yourself, you can have unforgettable moments and recover from painful experiences you thought you could never recover. I did that, and I am proud that I travelled alone and managed to recover from a painful break-up and see again that my life matters. That I can be happy with myself and enjoy the small gifts that life offers us every single day.
Ok then, travelling solo is great. But how about travelling solo and being a woman? Is it dangerous? What should you look out to be safe? My personal experience tells me that being a female solo traveller is not dangerous. Of course, I don't know how the things outside Europe are. I travelled in Greece, in Peloponnese, and everything was more than perfect. So, if you want to travel to Greece alone, these are my advices.

Solo female traveller
First of all, I think you should avoid get to drunk or walking around the streets late at night. I haven't met anyone, who scared me, but even in the safest place in the world, even in your country, being a woman and walking alone very late at night in dark streets isn't the safest thing to do.
On the other side, don't be afraid to talk to locals. Greek people are very hospitable, and they can help you out. Socialising is the easiest thing to do in Greece. People, young and old, will welcome you with their warm heartedness. Ask for advice, if you don't know where to eat or to drink coffee, and find the courage to speak to other people. The best place to meet new people is your hostel or hotel, but don't worry, you will have many opportunities to do that, if you are in Greece.
Being a female solo traveller has also advantages you can't imagine. Other women protect you, families invite you to their homes, and in general, no one is afraid of you. Furthermore, the good news are that in Greece, there are no certain rules about women, such as dressing in a appropriate way, like in Muslim countries. You can do whatever you want, and no one will put a label on you. Greek people are familiar with the travellers and can understand your craziness because they are crazy too.
Sexual harassment is the biggest fear of female solo travellers. I can reassure you that I didn't feel this fear because I was going in central, crowded places. Don't explore late at night a small, dark pebbled street and don't visit an infamous bar, which stands alone in a remote corner, and you will be just fine.
At last but not least, you don't have to worry about your hygiene. Greece is a European country, where you can find all the comfort and cleanliness you need. Just pick the right hotel or hostel, and everything is going to be all right!